DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~...

73
JAERI-Research 97-074 DEC 1 9 ESTIMATION OF COVARIANCES OF 16 0, 23Na, Fe, 235U, 238U AND 239PU NEUTRON NUCLEAR DATA IN JENDL-3.2 1 ... ,, ... ,-- ... - .... J ..... ....__.... _LI'I - -LI'I .....:.: .. : ..... ::. LI'I ru :::..:::...: ...... :.:.::: ..: .., LI'I C C Keiichi SHIBATA, Yutaka NAKAJIMA*, Toshihiko KAWANO**, Soo YouIOH*3, Hiroyuki MATSUNOBU*4 and Toru MURATA*5 Japan Atomic Energy Research Institute

Transcript of DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~...

Page 1: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

~ JAERI-Research ~

97-074

DEC 1 9 1997~

ESTIMATION OF COVARIANCES OF 160 23Na Fe 235U 238U AND 239PU

NEUTRON NUCLEAR DATA IN JENDL-32

1

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Keiichi SHIBATA Yutaka NAKAJIMA Toshihiko KA W ANO Soo YouIOH3 Hiroyuki MATSUNOBU4 and Toru MURATA5

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Japan Atomic Energy Research Institute

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Research 1997

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JAERI-Research 97-074

Estimation of Covariances of 160 23Na Fe 235U 238U and 239Pu

Neutron Nuclear Data in JENDL-32

Keiichi SHIBATA Yutaka NAKAJIMA Toshihiko KAWANO

Soo Youl OH3 Hiroyuki MATSUNOBU4 and Toru MURATA 5

Department of Reactor Engineering

Tokai Research Establishment

Japan Atomic Energy Research Institute

Tokai-mura Naka-gun Ibaraki-ken

(Received September 19 1997)

Covariances of nuclear data have been estimated for 6 nuclides contained in JENDL-32 The

nuclides considered are 160 23Na Fe 235U 238U and 239PU which are regarded as important for the

nuclear design study of fast reactors The physical quantities for which covariances are deduced are

cross sections resolved and unresolved resonance parameters and the first order Legendre-polynoshy

mial coefficient for the angular distribution of elastically scattered neutrons As for 235U covariances

were obtained also for the average number of neutrons emitted in fission The covariances were

estimated by using the same methodology that had been used in the JENDL-32 evaluation in order

to keep a consistency between mean values and their covariances The least-squares fitting code

GMA was used in estimating covariances for reactions of which JENDL-32 cross sections had been

evaluated by taking account of measurements In nuclear model calculations the covariances were

calculated by the KALMAN system The covariance data obtained were compiled in the ENDF-6

format and will be put into the JENDL-32 Covariance File which is one of JENDL special purpose

files

Keywords Covariance Nuclear Data JENDL-32 16023Na Fe 235U 238U 239PU Cross Section

Resonance Parameter Angular Distribution

Research Organization for Information Science and Technology

Kyushu University K U 3 Korea Atomic Energy Research Institute rlt A pound f 1 j~ c J 4 Data Engineering Inc

5 Nuclear Fuel Development Inc

JAERI-Research 97-074

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lAERI-Research 97-074

Contents

1 Introduction 1

2 Oxgen-16 2

3 Sodium-23 4

4 Natural Iron 6

5 Uranium-235 8

6 Uranium-238 13

7 Plutonium-239 16

8 Concluding Remarks 18

Acknowledgment 19

References 20

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JAERI-Research 97-074

1 Introduction

Uncertainties in nuclear data are needed not only to estimate margins in design

and safety of nuclear facilities but also to adjust group constants by considering critical

experiments The Nuclear Data Center of the Japan Atomic Energy Research Institute

(JAERI) has been involved in preparing the integrated group cross section library

promoted by the Power Reactor and Nuclear Fuel Development Corporation (PNC)

In the present work we estimated covariances of nuclear data for 160 23Na Fe

235U 238U and 239pU contained in JENDL-32 The physical quantities for which

covariances were estimated are cross sections resolved and unresolved resonance

parameters and the 1st order Legendre-polynomial coefficient for the elastic angular

distributions of neutrons As for 235U covariances were obtained also for the average

nUIuber of neutrons emitted in fission

The covariances were estimated on the basis of the same methods which had

been taken in the JENDL-32 evaluationl) The least-squares fitting code GMA2

which was developed at the Argonne National Laboratory was applied to estimate

covariances when the JENDL-32 data had been obtained by fitting to available

experimental data In cases where the JENDL-32 data are based on nuclear model

calculations the code system KALMAN3) which was developed at Kyushu University

was used to deduce uncertainties in model parameters Then the covariances of the

model calculations were obtained by using the law of error propagation On the

KALMAN system one can get covariances of cross sections and angular distributions

of emitted neutrons calculated from the optical model code ELIESE-34) the statistical

model codes CASTHy5) and EGNASH6) and the coupled-channel code ECIS7

)

In JENDL-32 the fission cross sections of 235U 238U and 239pU were obtained by

the simultaneous evaluation8) which took account of absolute and ratio measurements

The simultaneous evaluation yielded covariances as well as average cross sections

although the covariances were not compiled into JENDL-32 In the present work we

adopted the results obtained by the simultaneous evaluation without any modification

In this report we describe the methods of covariance estimation taken for each

nuclide together with the results obtained

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JAERI-Research 97 -07 4

2 Oxygen-16

Covariances were estimated for the total inelastic scattering (n2n) (nna)

1st(nnp) (nd) (n1) (np) and (na) cross sections and for the order Legendre

coefficient for the elastic angular distribution of neutrons In general the elastic

scattering cross section is obtained by subtracting partial cross sections from the total

cross section In such a case an NC-type sub-subsection is used to represent

covariances in the ENDF-format9) instead of actually estimating the covariance of the

elastic scattering cross section Following this procedure an NC-type subshy

subsection was made in the data file for 160 and the covariance of the elastic scattering

cross section can be calculated from those of other cross sections The same

procedure was applied to the covariances of the elastic scattering cross sections for

other nuclides in the present work

21 Covariance Estimation Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariance from the two sets of

measurements Cierjacks et al lO) and Larsonll ) It is found from Figs 1 and 2 that the

estimated error is consistent with the measurements and looks quite reasonable

2) (n2n) reaction cross section

The covariances were obtained from the measurements of Brill et al 12) In

JENDL-32 the cross section is ten times as large as the measurements because of a

compilation mistake Therefore the error was enlarged to cover the correct cross

section values

3) (nna) and (nnp) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations since there

exists no measurement However the parameters required as input to the model code

are no longer available Therefore in the present work we used the following rule

obtained by Oh13)

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lAERI-Research 97-074

Cross section 0 (mb) Standard deviation ()

500lt0 5

1~~500 10

1~0~100 15

0lt1 gt25

A full correlation was assumed since the JENDL-32 data were obtained from nuclear

model calculations and a strong correlation was expected in such calculations

4) (nd) reaction cross section

The covariances were obtained on the basis of the measurements of LillieI4)

The result is shown in Fig 3

5) (ny) reaction cross section

The covariances were estimated from the measurements of Wtist et al IS) and

Igashira et al 16) The result is shown in Fig 4

6) (np) reaction cross section

The covariances were estimated from the measurements of Borman et al 17gt

DeJuren and StooksberryI8) Seeman and MooreI9) and Martin20) The result is shown

in Fig 5

7) (na) reaction cross section

The covariances were estimated from the following experimental data

Nordborg et al2l) Davis et al 22gt Sick et a1 23gt Divatia et al24) Dickens and

Perey2S) Orphan et a126) and Bair and Haas27)

The result is shown in Fig 6 In the energy region above 7 MeV experimental data

are discrepant with each other

22 Covariance Estimation Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The CASTHY code yielded the covariances of the inelastic scattering cross

section using the KALMAN system The measurements of Nordborg et al21) were

used to deduce the uncertainties in the model parameters

2) Angular distributions for the elastic scattering

In JENDL-32 the angular distributions of elastically scattered neutrons were

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lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

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JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

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lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

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JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

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JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

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lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

- 13shy

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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JAERI-Research 97-074

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

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JAERI-Research 97-074

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- 24shy

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- 25shy

lAERI-Research 97 -074

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- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 2: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

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This report is issued irregularly

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Division Department of Intellectual Resources Japan Atomic Energy Research Institute

Tokai-mura Naka--gun Ibaraki-ken 319-11 Japan

Research 1997

B~ybIiJf~J-1Jf

P tf 6 ~ tIHiltl (l)

JAERI-Research 97-074

Estimation of Covariances of 160 23Na Fe 235U 238U and 239Pu

Neutron Nuclear Data in JENDL-32

Keiichi SHIBATA Yutaka NAKAJIMA Toshihiko KAWANO

Soo Youl OH3 Hiroyuki MATSUNOBU4 and Toru MURATA 5

Department of Reactor Engineering

Tokai Research Establishment

Japan Atomic Energy Research Institute

Tokai-mura Naka-gun Ibaraki-ken

(Received September 19 1997)

Covariances of nuclear data have been estimated for 6 nuclides contained in JENDL-32 The

nuclides considered are 160 23Na Fe 235U 238U and 239PU which are regarded as important for the

nuclear design study of fast reactors The physical quantities for which covariances are deduced are

cross sections resolved and unresolved resonance parameters and the first order Legendre-polynoshy

mial coefficient for the angular distribution of elastically scattered neutrons As for 235U covariances

were obtained also for the average number of neutrons emitted in fission The covariances were

estimated by using the same methodology that had been used in the JENDL-32 evaluation in order

to keep a consistency between mean values and their covariances The least-squares fitting code

GMA was used in estimating covariances for reactions of which JENDL-32 cross sections had been

evaluated by taking account of measurements In nuclear model calculations the covariances were

calculated by the KALMAN system The covariance data obtained were compiled in the ENDF-6

format and will be put into the JENDL-32 Covariance File which is one of JENDL special purpose

files

Keywords Covariance Nuclear Data JENDL-32 16023Na Fe 235U 238U 239PU Cross Section

Resonance Parameter Angular Distribution

Research Organization for Information Science and Technology

Kyushu University K U 3 Korea Atomic Energy Research Institute rlt A pound f 1 j~ c J 4 Data Engineering Inc

5 Nuclear Fuel Development Inc

JAERI-Research 97-074

B~~n~~m~~~m~~~I$$

~ffi m- middot lftm ~ iiiJf ~~ bull OH Soo You 1 3

~~ $ 4 bull Mffi fit 5

(19971F 9 ~ 19 B~Em)

J ENDL-3 2 ~JamprIi~tlL~~ 6~fiO)~T-70)~5t~~ttJElto xt~ctJt~fi

i~~~O)~St~t~~-c~~tJ 160 23Na Fe 235 U 23 8 U amprJ 2 3 9PU-C~ ~o ~5t~

irt3j(Q) intttoJEmiji lJTffiJf1i 5tbullbull ~~5t~~~1~5 j -7 amprJ5ff1~~U~tott ~ 1 lXO))t ~y

rtJilImi~-c~ ~o 235 U ~fJ l-r(i ~5t~~~j ~ Sfl~lfttt~~~~O)~5t~ b3j(Q) i

nto ~5t~mJE~ ~~ -r (i J END L - 3 2 0)~1iffi ~ffl ~ i nt 0) c 101 t J~iJffl ~ i n

to J END L - 3 2 -c4t i n -r~ ~ampJDltJTffiJ~ir~~1~~~3j(Q) i nt~~i MJEJ 71 YT1 7~J- rGMA~ffl~~5t~~ttlElto -J Em~~t1O)~5t~(iKALMAN

~ATb~~ ~ ~tlto ~ ~ -C1~ int~5t~T-7 (i END F - 6 7 -7 Y r-C7 7 -1 )t

1t~ n J END L~~sect1yenJ7 7 -1 )tO) 1 --gt-C~ ~ J END L 3 2 ~5t~7 7 -1 )t~JampR~ n

iiUJf~PJT =319-11 ~~lfUJ~fiiJi~ii1tl1JBN 2 4

(M) ~lt~~f-~tt~rUJf~m

3 ~JJR-=ftJUJf~PJT 4 (f) T-7I~

5 (f) B~~flrm~

ii

lAERI-Research 97-074

Contents

1 Introduction 1

2 Oxgen-16 2

3 Sodium-23 4

4 Natural Iron 6

5 Uranium-235 8

6 Uranium-238 13

7 Plutonium-239 16

8 Concluding Remarks 18

Acknowledgment 19

References 20

sect

1 t t tIJ bullbull bullbull bullbull bull bull bull bullbull bull bull bull bullbull bullbull bullbull bull bullbullbullbull bull bull bull bull bullbull bull bull bull bull 1

2 ~~-16 2

3 -)- ~ I) ry L-23 4

4 ~~~ 6

5 ry 5 -235 8

6 ry 5 -238 13

7 -jJJ ~ ry L-239 16

8 E ~ 18

~ ~$ 19

20

iii

JAERI-Research 97-074

1 Introduction

Uncertainties in nuclear data are needed not only to estimate margins in design

and safety of nuclear facilities but also to adjust group constants by considering critical

experiments The Nuclear Data Center of the Japan Atomic Energy Research Institute

(JAERI) has been involved in preparing the integrated group cross section library

promoted by the Power Reactor and Nuclear Fuel Development Corporation (PNC)

In the present work we estimated covariances of nuclear data for 160 23Na Fe

235U 238U and 239pU contained in JENDL-32 The physical quantities for which

covariances were estimated are cross sections resolved and unresolved resonance

parameters and the 1st order Legendre-polynomial coefficient for the elastic angular

distributions of neutrons As for 235U covariances were obtained also for the average

nUIuber of neutrons emitted in fission

The covariances were estimated on the basis of the same methods which had

been taken in the JENDL-32 evaluationl) The least-squares fitting code GMA2

which was developed at the Argonne National Laboratory was applied to estimate

covariances when the JENDL-32 data had been obtained by fitting to available

experimental data In cases where the JENDL-32 data are based on nuclear model

calculations the code system KALMAN3) which was developed at Kyushu University

was used to deduce uncertainties in model parameters Then the covariances of the

model calculations were obtained by using the law of error propagation On the

KALMAN system one can get covariances of cross sections and angular distributions

of emitted neutrons calculated from the optical model code ELIESE-34) the statistical

model codes CASTHy5) and EGNASH6) and the coupled-channel code ECIS7

)

In JENDL-32 the fission cross sections of 235U 238U and 239pU were obtained by

the simultaneous evaluation8) which took account of absolute and ratio measurements

The simultaneous evaluation yielded covariances as well as average cross sections

although the covariances were not compiled into JENDL-32 In the present work we

adopted the results obtained by the simultaneous evaluation without any modification

In this report we describe the methods of covariance estimation taken for each

nuclide together with the results obtained

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JAERI-Research 97 -07 4

2 Oxygen-16

Covariances were estimated for the total inelastic scattering (n2n) (nna)

1st(nnp) (nd) (n1) (np) and (na) cross sections and for the order Legendre

coefficient for the elastic angular distribution of neutrons In general the elastic

scattering cross section is obtained by subtracting partial cross sections from the total

cross section In such a case an NC-type sub-subsection is used to represent

covariances in the ENDF-format9) instead of actually estimating the covariance of the

elastic scattering cross section Following this procedure an NC-type subshy

subsection was made in the data file for 160 and the covariance of the elastic scattering

cross section can be calculated from those of other cross sections The same

procedure was applied to the covariances of the elastic scattering cross sections for

other nuclides in the present work

21 Covariance Estimation Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariance from the two sets of

measurements Cierjacks et al lO) and Larsonll ) It is found from Figs 1 and 2 that the

estimated error is consistent with the measurements and looks quite reasonable

2) (n2n) reaction cross section

The covariances were obtained from the measurements of Brill et al 12) In

JENDL-32 the cross section is ten times as large as the measurements because of a

compilation mistake Therefore the error was enlarged to cover the correct cross

section values

3) (nna) and (nnp) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations since there

exists no measurement However the parameters required as input to the model code

are no longer available Therefore in the present work we used the following rule

obtained by Oh13)

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lAERI-Research 97-074

Cross section 0 (mb) Standard deviation ()

500lt0 5

1~~500 10

1~0~100 15

0lt1 gt25

A full correlation was assumed since the JENDL-32 data were obtained from nuclear

model calculations and a strong correlation was expected in such calculations

4) (nd) reaction cross section

The covariances were obtained on the basis of the measurements of LillieI4)

The result is shown in Fig 3

5) (ny) reaction cross section

The covariances were estimated from the measurements of Wtist et al IS) and

Igashira et al 16) The result is shown in Fig 4

6) (np) reaction cross section

The covariances were estimated from the measurements of Borman et al 17gt

DeJuren and StooksberryI8) Seeman and MooreI9) and Martin20) The result is shown

in Fig 5

7) (na) reaction cross section

The covariances were estimated from the following experimental data

Nordborg et al2l) Davis et al 22gt Sick et a1 23gt Divatia et al24) Dickens and

Perey2S) Orphan et a126) and Bair and Haas27)

The result is shown in Fig 6 In the energy region above 7 MeV experimental data

are discrepant with each other

22 Covariance Estimation Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The CASTHY code yielded the covariances of the inelastic scattering cross

section using the KALMAN system The measurements of Nordborg et al21) were

used to deduce the uncertainties in the model parameters

2) Angular distributions for the elastic scattering

In JENDL-32 the angular distributions of elastically scattered neutrons were

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lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

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JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

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lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

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JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

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JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

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lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

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lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

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lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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lAERI-Research 97-074

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JAERI-Research 97-074

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Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

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136) Gwin R et al Nucl Sci Eng 81 381 (1984)

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- 24shy

lAERI-Research 97-074

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- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

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192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 3: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

Estimation of Covariances of 160 23Na Fe 235U 238U and 239Pu

Neutron Nuclear Data in JENDL-32

Keiichi SHIBATA Yutaka NAKAJIMA Toshihiko KAWANO

Soo Youl OH3 Hiroyuki MATSUNOBU4 and Toru MURATA 5

Department of Reactor Engineering

Tokai Research Establishment

Japan Atomic Energy Research Institute

Tokai-mura Naka-gun Ibaraki-ken

(Received September 19 1997)

Covariances of nuclear data have been estimated for 6 nuclides contained in JENDL-32 The

nuclides considered are 160 23Na Fe 235U 238U and 239PU which are regarded as important for the

nuclear design study of fast reactors The physical quantities for which covariances are deduced are

cross sections resolved and unresolved resonance parameters and the first order Legendre-polynoshy

mial coefficient for the angular distribution of elastically scattered neutrons As for 235U covariances

were obtained also for the average number of neutrons emitted in fission The covariances were

estimated by using the same methodology that had been used in the JENDL-32 evaluation in order

to keep a consistency between mean values and their covariances The least-squares fitting code

GMA was used in estimating covariances for reactions of which JENDL-32 cross sections had been

evaluated by taking account of measurements In nuclear model calculations the covariances were

calculated by the KALMAN system The covariance data obtained were compiled in the ENDF-6

format and will be put into the JENDL-32 Covariance File which is one of JENDL special purpose

files

Keywords Covariance Nuclear Data JENDL-32 16023Na Fe 235U 238U 239PU Cross Section

Resonance Parameter Angular Distribution

Research Organization for Information Science and Technology

Kyushu University K U 3 Korea Atomic Energy Research Institute rlt A pound f 1 j~ c J 4 Data Engineering Inc

5 Nuclear Fuel Development Inc

JAERI-Research 97-074

B~~n~~m~~~m~~~I$$

~ffi m- middot lftm ~ iiiJf ~~ bull OH Soo You 1 3

~~ $ 4 bull Mffi fit 5

(19971F 9 ~ 19 B~Em)

J ENDL-3 2 ~JamprIi~tlL~~ 6~fiO)~T-70)~5t~~ttJElto xt~ctJt~fi

i~~~O)~St~t~~-c~~tJ 160 23Na Fe 235 U 23 8 U amprJ 2 3 9PU-C~ ~o ~5t~

irt3j(Q) intttoJEmiji lJTffiJf1i 5tbullbull ~~5t~~~1~5 j -7 amprJ5ff1~~U~tott ~ 1 lXO))t ~y

rtJilImi~-c~ ~o 235 U ~fJ l-r(i ~5t~~~j ~ Sfl~lfttt~~~~O)~5t~ b3j(Q) i

nto ~5t~mJE~ ~~ -r (i J END L - 3 2 0)~1iffi ~ffl ~ i nt 0) c 101 t J~iJffl ~ i n

to J END L - 3 2 -c4t i n -r~ ~ampJDltJTffiJ~ir~~1~~~3j(Q) i nt~~i MJEJ 71 YT1 7~J- rGMA~ffl~~5t~~ttlElto -J Em~~t1O)~5t~(iKALMAN

~ATb~~ ~ ~tlto ~ ~ -C1~ int~5t~T-7 (i END F - 6 7 -7 Y r-C7 7 -1 )t

1t~ n J END L~~sect1yenJ7 7 -1 )tO) 1 --gt-C~ ~ J END L 3 2 ~5t~7 7 -1 )t~JampR~ n

iiUJf~PJT =319-11 ~~lfUJ~fiiJi~ii1tl1JBN 2 4

(M) ~lt~~f-~tt~rUJf~m

3 ~JJR-=ftJUJf~PJT 4 (f) T-7I~

5 (f) B~~flrm~

ii

lAERI-Research 97-074

Contents

1 Introduction 1

2 Oxgen-16 2

3 Sodium-23 4

4 Natural Iron 6

5 Uranium-235 8

6 Uranium-238 13

7 Plutonium-239 16

8 Concluding Remarks 18

Acknowledgment 19

References 20

sect

1 t t tIJ bullbull bullbull bullbull bull bull bull bullbull bull bull bull bullbull bullbull bullbull bull bullbullbullbull bull bull bull bull bullbull bull bull bull bull 1

2 ~~-16 2

3 -)- ~ I) ry L-23 4

4 ~~~ 6

5 ry 5 -235 8

6 ry 5 -238 13

7 -jJJ ~ ry L-239 16

8 E ~ 18

~ ~$ 19

20

iii

JAERI-Research 97-074

1 Introduction

Uncertainties in nuclear data are needed not only to estimate margins in design

and safety of nuclear facilities but also to adjust group constants by considering critical

experiments The Nuclear Data Center of the Japan Atomic Energy Research Institute

(JAERI) has been involved in preparing the integrated group cross section library

promoted by the Power Reactor and Nuclear Fuel Development Corporation (PNC)

In the present work we estimated covariances of nuclear data for 160 23Na Fe

235U 238U and 239pU contained in JENDL-32 The physical quantities for which

covariances were estimated are cross sections resolved and unresolved resonance

parameters and the 1st order Legendre-polynomial coefficient for the elastic angular

distributions of neutrons As for 235U covariances were obtained also for the average

nUIuber of neutrons emitted in fission

The covariances were estimated on the basis of the same methods which had

been taken in the JENDL-32 evaluationl) The least-squares fitting code GMA2

which was developed at the Argonne National Laboratory was applied to estimate

covariances when the JENDL-32 data had been obtained by fitting to available

experimental data In cases where the JENDL-32 data are based on nuclear model

calculations the code system KALMAN3) which was developed at Kyushu University

was used to deduce uncertainties in model parameters Then the covariances of the

model calculations were obtained by using the law of error propagation On the

KALMAN system one can get covariances of cross sections and angular distributions

of emitted neutrons calculated from the optical model code ELIESE-34) the statistical

model codes CASTHy5) and EGNASH6) and the coupled-channel code ECIS7

)

In JENDL-32 the fission cross sections of 235U 238U and 239pU were obtained by

the simultaneous evaluation8) which took account of absolute and ratio measurements

The simultaneous evaluation yielded covariances as well as average cross sections

although the covariances were not compiled into JENDL-32 In the present work we

adopted the results obtained by the simultaneous evaluation without any modification

In this report we describe the methods of covariance estimation taken for each

nuclide together with the results obtained

- 1 shy

JAERI-Research 97 -07 4

2 Oxygen-16

Covariances were estimated for the total inelastic scattering (n2n) (nna)

1st(nnp) (nd) (n1) (np) and (na) cross sections and for the order Legendre

coefficient for the elastic angular distribution of neutrons In general the elastic

scattering cross section is obtained by subtracting partial cross sections from the total

cross section In such a case an NC-type sub-subsection is used to represent

covariances in the ENDF-format9) instead of actually estimating the covariance of the

elastic scattering cross section Following this procedure an NC-type subshy

subsection was made in the data file for 160 and the covariance of the elastic scattering

cross section can be calculated from those of other cross sections The same

procedure was applied to the covariances of the elastic scattering cross sections for

other nuclides in the present work

21 Covariance Estimation Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariance from the two sets of

measurements Cierjacks et al lO) and Larsonll ) It is found from Figs 1 and 2 that the

estimated error is consistent with the measurements and looks quite reasonable

2) (n2n) reaction cross section

The covariances were obtained from the measurements of Brill et al 12) In

JENDL-32 the cross section is ten times as large as the measurements because of a

compilation mistake Therefore the error was enlarged to cover the correct cross

section values

3) (nna) and (nnp) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations since there

exists no measurement However the parameters required as input to the model code

are no longer available Therefore in the present work we used the following rule

obtained by Oh13)

- 2 shy

lAERI-Research 97-074

Cross section 0 (mb) Standard deviation ()

500lt0 5

1~~500 10

1~0~100 15

0lt1 gt25

A full correlation was assumed since the JENDL-32 data were obtained from nuclear

model calculations and a strong correlation was expected in such calculations

4) (nd) reaction cross section

The covariances were obtained on the basis of the measurements of LillieI4)

The result is shown in Fig 3

5) (ny) reaction cross section

The covariances were estimated from the measurements of Wtist et al IS) and

Igashira et al 16) The result is shown in Fig 4

6) (np) reaction cross section

The covariances were estimated from the measurements of Borman et al 17gt

DeJuren and StooksberryI8) Seeman and MooreI9) and Martin20) The result is shown

in Fig 5

7) (na) reaction cross section

The covariances were estimated from the following experimental data

Nordborg et al2l) Davis et al 22gt Sick et a1 23gt Divatia et al24) Dickens and

Perey2S) Orphan et a126) and Bair and Haas27)

The result is shown in Fig 6 In the energy region above 7 MeV experimental data

are discrepant with each other

22 Covariance Estimation Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The CASTHY code yielded the covariances of the inelastic scattering cross

section using the KALMAN system The measurements of Nordborg et al21) were

used to deduce the uncertainties in the model parameters

2) Angular distributions for the elastic scattering

In JENDL-32 the angular distributions of elastically scattered neutrons were

- 3 shy

~---~~-~---------------------

lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

-4shy

JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

-5shy

lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

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JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

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JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

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lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

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lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

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JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

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JAERI-Research 97-074

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JAERI-Research 97-074

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Parameters of 56Fe 239Pu 240pU and 238U JAERI-Research 97-035 (1997) [in

Japanese]

94) Carlson AD and Cerbone RJ Nucl Sci Eng 42 28 (1970)

95) Cierjacks S et al KFK-1000 (1969)

96) Perey FG et al ORNL-4823 (1972)

97) Pattenden NJ et al AERE-R-7425 (1973)

98) Schwartz RB et al NBS-MONO-138 (1974)

99) Terrel J and Holm DM Phys Rev102 2031 (1958)

100) Bormann M et al Z Phys 166477 (1962)

101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

102) Liskien H and Paulsen A Nukleonik8 315 (1966)

103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

104) Ryves TB et al Metrologia14 127 (1978)

105) Ikeda Y et al JAERI-1312 (1988)

106) Li Chi-chou et al INDC(CPR)-16 (1989)

107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

108) Hopkins JC and Gilbert MG Nucl Sci Eng 12 431 (1964)

109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

238 Proc Int Conf Nuclear Physics Berkley 1980 LBL-11118 p243 (1980)

112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

(1962)

115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

- 23shy

JAERI-Research 97-074

116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

(1984)

121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

165 Vol 1 (1967)

122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

131) CorviF et al NEANDC(E) 232U VolllEuratom P5 (1981)

132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

- 24shy

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 4: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

B~~n~~m~~~m~~~I$$

~ffi m- middot lftm ~ iiiJf ~~ bull OH Soo You 1 3

~~ $ 4 bull Mffi fit 5

(19971F 9 ~ 19 B~Em)

J ENDL-3 2 ~JamprIi~tlL~~ 6~fiO)~T-70)~5t~~ttJElto xt~ctJt~fi

i~~~O)~St~t~~-c~~tJ 160 23Na Fe 235 U 23 8 U amprJ 2 3 9PU-C~ ~o ~5t~

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to J END L - 3 2 -c4t i n -r~ ~ampJDltJTffiJ~ir~~1~~~3j(Q) i nt~~i MJEJ 71 YT1 7~J- rGMA~ffl~~5t~~ttlElto -J Em~~t1O)~5t~(iKALMAN

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5 (f) B~~flrm~

ii

lAERI-Research 97-074

Contents

1 Introduction 1

2 Oxgen-16 2

3 Sodium-23 4

4 Natural Iron 6

5 Uranium-235 8

6 Uranium-238 13

7 Plutonium-239 16

8 Concluding Remarks 18

Acknowledgment 19

References 20

sect

1 t t tIJ bullbull bullbull bullbull bull bull bull bullbull bull bull bull bullbull bullbull bullbull bull bullbullbullbull bull bull bull bull bullbull bull bull bull bull 1

2 ~~-16 2

3 -)- ~ I) ry L-23 4

4 ~~~ 6

5 ry 5 -235 8

6 ry 5 -238 13

7 -jJJ ~ ry L-239 16

8 E ~ 18

~ ~$ 19

20

iii

JAERI-Research 97-074

1 Introduction

Uncertainties in nuclear data are needed not only to estimate margins in design

and safety of nuclear facilities but also to adjust group constants by considering critical

experiments The Nuclear Data Center of the Japan Atomic Energy Research Institute

(JAERI) has been involved in preparing the integrated group cross section library

promoted by the Power Reactor and Nuclear Fuel Development Corporation (PNC)

In the present work we estimated covariances of nuclear data for 160 23Na Fe

235U 238U and 239pU contained in JENDL-32 The physical quantities for which

covariances were estimated are cross sections resolved and unresolved resonance

parameters and the 1st order Legendre-polynomial coefficient for the elastic angular

distributions of neutrons As for 235U covariances were obtained also for the average

nUIuber of neutrons emitted in fission

The covariances were estimated on the basis of the same methods which had

been taken in the JENDL-32 evaluationl) The least-squares fitting code GMA2

which was developed at the Argonne National Laboratory was applied to estimate

covariances when the JENDL-32 data had been obtained by fitting to available

experimental data In cases where the JENDL-32 data are based on nuclear model

calculations the code system KALMAN3) which was developed at Kyushu University

was used to deduce uncertainties in model parameters Then the covariances of the

model calculations were obtained by using the law of error propagation On the

KALMAN system one can get covariances of cross sections and angular distributions

of emitted neutrons calculated from the optical model code ELIESE-34) the statistical

model codes CASTHy5) and EGNASH6) and the coupled-channel code ECIS7

)

In JENDL-32 the fission cross sections of 235U 238U and 239pU were obtained by

the simultaneous evaluation8) which took account of absolute and ratio measurements

The simultaneous evaluation yielded covariances as well as average cross sections

although the covariances were not compiled into JENDL-32 In the present work we

adopted the results obtained by the simultaneous evaluation without any modification

In this report we describe the methods of covariance estimation taken for each

nuclide together with the results obtained

- 1 shy

JAERI-Research 97 -07 4

2 Oxygen-16

Covariances were estimated for the total inelastic scattering (n2n) (nna)

1st(nnp) (nd) (n1) (np) and (na) cross sections and for the order Legendre

coefficient for the elastic angular distribution of neutrons In general the elastic

scattering cross section is obtained by subtracting partial cross sections from the total

cross section In such a case an NC-type sub-subsection is used to represent

covariances in the ENDF-format9) instead of actually estimating the covariance of the

elastic scattering cross section Following this procedure an NC-type subshy

subsection was made in the data file for 160 and the covariance of the elastic scattering

cross section can be calculated from those of other cross sections The same

procedure was applied to the covariances of the elastic scattering cross sections for

other nuclides in the present work

21 Covariance Estimation Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariance from the two sets of

measurements Cierjacks et al lO) and Larsonll ) It is found from Figs 1 and 2 that the

estimated error is consistent with the measurements and looks quite reasonable

2) (n2n) reaction cross section

The covariances were obtained from the measurements of Brill et al 12) In

JENDL-32 the cross section is ten times as large as the measurements because of a

compilation mistake Therefore the error was enlarged to cover the correct cross

section values

3) (nna) and (nnp) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations since there

exists no measurement However the parameters required as input to the model code

are no longer available Therefore in the present work we used the following rule

obtained by Oh13)

- 2 shy

lAERI-Research 97-074

Cross section 0 (mb) Standard deviation ()

500lt0 5

1~~500 10

1~0~100 15

0lt1 gt25

A full correlation was assumed since the JENDL-32 data were obtained from nuclear

model calculations and a strong correlation was expected in such calculations

4) (nd) reaction cross section

The covariances were obtained on the basis of the measurements of LillieI4)

The result is shown in Fig 3

5) (ny) reaction cross section

The covariances were estimated from the measurements of Wtist et al IS) and

Igashira et al 16) The result is shown in Fig 4

6) (np) reaction cross section

The covariances were estimated from the measurements of Borman et al 17gt

DeJuren and StooksberryI8) Seeman and MooreI9) and Martin20) The result is shown

in Fig 5

7) (na) reaction cross section

The covariances were estimated from the following experimental data

Nordborg et al2l) Davis et al 22gt Sick et a1 23gt Divatia et al24) Dickens and

Perey2S) Orphan et a126) and Bair and Haas27)

The result is shown in Fig 6 In the energy region above 7 MeV experimental data

are discrepant with each other

22 Covariance Estimation Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The CASTHY code yielded the covariances of the inelastic scattering cross

section using the KALMAN system The measurements of Nordborg et al21) were

used to deduce the uncertainties in the model parameters

2) Angular distributions for the elastic scattering

In JENDL-32 the angular distributions of elastically scattered neutrons were

- 3 shy

~---~~-~---------------------

lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

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JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

-5shy

lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

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JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

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JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

-10 shy

lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

- 11shy

JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

-12shy

JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

- 13shy

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

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- 25shy

lAERI-Research 97 -074

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- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 5: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

Contents

1 Introduction 1

2 Oxgen-16 2

3 Sodium-23 4

4 Natural Iron 6

5 Uranium-235 8

6 Uranium-238 13

7 Plutonium-239 16

8 Concluding Remarks 18

Acknowledgment 19

References 20

sect

1 t t tIJ bullbull bullbull bullbull bull bull bull bullbull bull bull bull bullbull bullbull bullbull bull bullbullbullbull bull bull bull bull bullbull bull bull bull bull 1

2 ~~-16 2

3 -)- ~ I) ry L-23 4

4 ~~~ 6

5 ry 5 -235 8

6 ry 5 -238 13

7 -jJJ ~ ry L-239 16

8 E ~ 18

~ ~$ 19

20

iii

JAERI-Research 97-074

1 Introduction

Uncertainties in nuclear data are needed not only to estimate margins in design

and safety of nuclear facilities but also to adjust group constants by considering critical

experiments The Nuclear Data Center of the Japan Atomic Energy Research Institute

(JAERI) has been involved in preparing the integrated group cross section library

promoted by the Power Reactor and Nuclear Fuel Development Corporation (PNC)

In the present work we estimated covariances of nuclear data for 160 23Na Fe

235U 238U and 239pU contained in JENDL-32 The physical quantities for which

covariances were estimated are cross sections resolved and unresolved resonance

parameters and the 1st order Legendre-polynomial coefficient for the elastic angular

distributions of neutrons As for 235U covariances were obtained also for the average

nUIuber of neutrons emitted in fission

The covariances were estimated on the basis of the same methods which had

been taken in the JENDL-32 evaluationl) The least-squares fitting code GMA2

which was developed at the Argonne National Laboratory was applied to estimate

covariances when the JENDL-32 data had been obtained by fitting to available

experimental data In cases where the JENDL-32 data are based on nuclear model

calculations the code system KALMAN3) which was developed at Kyushu University

was used to deduce uncertainties in model parameters Then the covariances of the

model calculations were obtained by using the law of error propagation On the

KALMAN system one can get covariances of cross sections and angular distributions

of emitted neutrons calculated from the optical model code ELIESE-34) the statistical

model codes CASTHy5) and EGNASH6) and the coupled-channel code ECIS7

)

In JENDL-32 the fission cross sections of 235U 238U and 239pU were obtained by

the simultaneous evaluation8) which took account of absolute and ratio measurements

The simultaneous evaluation yielded covariances as well as average cross sections

although the covariances were not compiled into JENDL-32 In the present work we

adopted the results obtained by the simultaneous evaluation without any modification

In this report we describe the methods of covariance estimation taken for each

nuclide together with the results obtained

- 1 shy

JAERI-Research 97 -07 4

2 Oxygen-16

Covariances were estimated for the total inelastic scattering (n2n) (nna)

1st(nnp) (nd) (n1) (np) and (na) cross sections and for the order Legendre

coefficient for the elastic angular distribution of neutrons In general the elastic

scattering cross section is obtained by subtracting partial cross sections from the total

cross section In such a case an NC-type sub-subsection is used to represent

covariances in the ENDF-format9) instead of actually estimating the covariance of the

elastic scattering cross section Following this procedure an NC-type subshy

subsection was made in the data file for 160 and the covariance of the elastic scattering

cross section can be calculated from those of other cross sections The same

procedure was applied to the covariances of the elastic scattering cross sections for

other nuclides in the present work

21 Covariance Estimation Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariance from the two sets of

measurements Cierjacks et al lO) and Larsonll ) It is found from Figs 1 and 2 that the

estimated error is consistent with the measurements and looks quite reasonable

2) (n2n) reaction cross section

The covariances were obtained from the measurements of Brill et al 12) In

JENDL-32 the cross section is ten times as large as the measurements because of a

compilation mistake Therefore the error was enlarged to cover the correct cross

section values

3) (nna) and (nnp) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations since there

exists no measurement However the parameters required as input to the model code

are no longer available Therefore in the present work we used the following rule

obtained by Oh13)

- 2 shy

lAERI-Research 97-074

Cross section 0 (mb) Standard deviation ()

500lt0 5

1~~500 10

1~0~100 15

0lt1 gt25

A full correlation was assumed since the JENDL-32 data were obtained from nuclear

model calculations and a strong correlation was expected in such calculations

4) (nd) reaction cross section

The covariances were obtained on the basis of the measurements of LillieI4)

The result is shown in Fig 3

5) (ny) reaction cross section

The covariances were estimated from the measurements of Wtist et al IS) and

Igashira et al 16) The result is shown in Fig 4

6) (np) reaction cross section

The covariances were estimated from the measurements of Borman et al 17gt

DeJuren and StooksberryI8) Seeman and MooreI9) and Martin20) The result is shown

in Fig 5

7) (na) reaction cross section

The covariances were estimated from the following experimental data

Nordborg et al2l) Davis et al 22gt Sick et a1 23gt Divatia et al24) Dickens and

Perey2S) Orphan et a126) and Bair and Haas27)

The result is shown in Fig 6 In the energy region above 7 MeV experimental data

are discrepant with each other

22 Covariance Estimation Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The CASTHY code yielded the covariances of the inelastic scattering cross

section using the KALMAN system The measurements of Nordborg et al21) were

used to deduce the uncertainties in the model parameters

2) Angular distributions for the elastic scattering

In JENDL-32 the angular distributions of elastically scattered neutrons were

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lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

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JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

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lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

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JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

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JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

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lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

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lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

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JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

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JAERI-Research 97-074

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10) Cierjacks S et al Nucl Instrum Meth~ 185 (1980)

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NCS-51245 p 277 (1980)

12) Brill OD et al Sov Phys Doklady 624 (1961)

13) Oh SY and Shibata K Private communication (1996)

14) Lillie AB Phys Rev 81 716 (1952)

15) Wilst N et al Phys Rev Cl2 1153 (1979)

16) Igashira M et al Ap J 44l L89 (1995)

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JAERI-Research 97-074

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26) Orphan VJ et al Nucl Sci Eng 42 352 (1970)

27) Bair JK and Haas FX Phys Rev C] 1356 (1973)

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80) Ngoc PN et al Private communication (1980)

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

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88) Fasoli U et al Nucl Phys Al25 227(1969)

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Meeting on Neutron Data of Structural Materials for Fast Reactors Geel 1977

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96) Perey FG et al ORNL-4823 (1972)

97) Pattenden NJ et al AERE-R-7425 (1973)

98) Schwartz RB et al NBS-MONO-138 (1974)

99) Terrel J and Holm DM Phys Rev102 2031 (1958)

100) Bormann M et al Z Phys 166477 (1962)

101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

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103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

104) Ryves TB et al Metrologia14 127 (1978)

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107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

108) Hopkins JC and Gilbert MG Nucl Sci Eng 12 431 (1964)

109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

238 Proc Int Conf Nuclear Physics Berkley 1980 LBL-11118 p243 (1980)

112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

(1962)

115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

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116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

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121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

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122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

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Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

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132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

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lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

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1979 p 677 (1980)

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19881-282 (1988)

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164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

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169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 6: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

1 Introduction

Uncertainties in nuclear data are needed not only to estimate margins in design

and safety of nuclear facilities but also to adjust group constants by considering critical

experiments The Nuclear Data Center of the Japan Atomic Energy Research Institute

(JAERI) has been involved in preparing the integrated group cross section library

promoted by the Power Reactor and Nuclear Fuel Development Corporation (PNC)

In the present work we estimated covariances of nuclear data for 160 23Na Fe

235U 238U and 239pU contained in JENDL-32 The physical quantities for which

covariances were estimated are cross sections resolved and unresolved resonance

parameters and the 1st order Legendre-polynomial coefficient for the elastic angular

distributions of neutrons As for 235U covariances were obtained also for the average

nUIuber of neutrons emitted in fission

The covariances were estimated on the basis of the same methods which had

been taken in the JENDL-32 evaluationl) The least-squares fitting code GMA2

which was developed at the Argonne National Laboratory was applied to estimate

covariances when the JENDL-32 data had been obtained by fitting to available

experimental data In cases where the JENDL-32 data are based on nuclear model

calculations the code system KALMAN3) which was developed at Kyushu University

was used to deduce uncertainties in model parameters Then the covariances of the

model calculations were obtained by using the law of error propagation On the

KALMAN system one can get covariances of cross sections and angular distributions

of emitted neutrons calculated from the optical model code ELIESE-34) the statistical

model codes CASTHy5) and EGNASH6) and the coupled-channel code ECIS7

)

In JENDL-32 the fission cross sections of 235U 238U and 239pU were obtained by

the simultaneous evaluation8) which took account of absolute and ratio measurements

The simultaneous evaluation yielded covariances as well as average cross sections

although the covariances were not compiled into JENDL-32 In the present work we

adopted the results obtained by the simultaneous evaluation without any modification

In this report we describe the methods of covariance estimation taken for each

nuclide together with the results obtained

- 1 shy

JAERI-Research 97 -07 4

2 Oxygen-16

Covariances were estimated for the total inelastic scattering (n2n) (nna)

1st(nnp) (nd) (n1) (np) and (na) cross sections and for the order Legendre

coefficient for the elastic angular distribution of neutrons In general the elastic

scattering cross section is obtained by subtracting partial cross sections from the total

cross section In such a case an NC-type sub-subsection is used to represent

covariances in the ENDF-format9) instead of actually estimating the covariance of the

elastic scattering cross section Following this procedure an NC-type subshy

subsection was made in the data file for 160 and the covariance of the elastic scattering

cross section can be calculated from those of other cross sections The same

procedure was applied to the covariances of the elastic scattering cross sections for

other nuclides in the present work

21 Covariance Estimation Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariance from the two sets of

measurements Cierjacks et al lO) and Larsonll ) It is found from Figs 1 and 2 that the

estimated error is consistent with the measurements and looks quite reasonable

2) (n2n) reaction cross section

The covariances were obtained from the measurements of Brill et al 12) In

JENDL-32 the cross section is ten times as large as the measurements because of a

compilation mistake Therefore the error was enlarged to cover the correct cross

section values

3) (nna) and (nnp) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations since there

exists no measurement However the parameters required as input to the model code

are no longer available Therefore in the present work we used the following rule

obtained by Oh13)

- 2 shy

lAERI-Research 97-074

Cross section 0 (mb) Standard deviation ()

500lt0 5

1~~500 10

1~0~100 15

0lt1 gt25

A full correlation was assumed since the JENDL-32 data were obtained from nuclear

model calculations and a strong correlation was expected in such calculations

4) (nd) reaction cross section

The covariances were obtained on the basis of the measurements of LillieI4)

The result is shown in Fig 3

5) (ny) reaction cross section

The covariances were estimated from the measurements of Wtist et al IS) and

Igashira et al 16) The result is shown in Fig 4

6) (np) reaction cross section

The covariances were estimated from the measurements of Borman et al 17gt

DeJuren and StooksberryI8) Seeman and MooreI9) and Martin20) The result is shown

in Fig 5

7) (na) reaction cross section

The covariances were estimated from the following experimental data

Nordborg et al2l) Davis et al 22gt Sick et a1 23gt Divatia et al24) Dickens and

Perey2S) Orphan et a126) and Bair and Haas27)

The result is shown in Fig 6 In the energy region above 7 MeV experimental data

are discrepant with each other

22 Covariance Estimation Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The CASTHY code yielded the covariances of the inelastic scattering cross

section using the KALMAN system The measurements of Nordborg et al21) were

used to deduce the uncertainties in the model parameters

2) Angular distributions for the elastic scattering

In JENDL-32 the angular distributions of elastically scattered neutrons were

- 3 shy

~---~~-~---------------------

lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

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JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

-5shy

lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

-6shy

JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

-7shy

JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

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lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

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JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

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JAERI-Research 97-074

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JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 7: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97 -07 4

2 Oxygen-16

Covariances were estimated for the total inelastic scattering (n2n) (nna)

1st(nnp) (nd) (n1) (np) and (na) cross sections and for the order Legendre

coefficient for the elastic angular distribution of neutrons In general the elastic

scattering cross section is obtained by subtracting partial cross sections from the total

cross section In such a case an NC-type sub-subsection is used to represent

covariances in the ENDF-format9) instead of actually estimating the covariance of the

elastic scattering cross section Following this procedure an NC-type subshy

subsection was made in the data file for 160 and the covariance of the elastic scattering

cross section can be calculated from those of other cross sections The same

procedure was applied to the covariances of the elastic scattering cross sections for

other nuclides in the present work

21 Covariance Estimation Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariance from the two sets of

measurements Cierjacks et al lO) and Larsonll ) It is found from Figs 1 and 2 that the

estimated error is consistent with the measurements and looks quite reasonable

2) (n2n) reaction cross section

The covariances were obtained from the measurements of Brill et al 12) In

JENDL-32 the cross section is ten times as large as the measurements because of a

compilation mistake Therefore the error was enlarged to cover the correct cross

section values

3) (nna) and (nnp) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations since there

exists no measurement However the parameters required as input to the model code

are no longer available Therefore in the present work we used the following rule

obtained by Oh13)

- 2 shy

lAERI-Research 97-074

Cross section 0 (mb) Standard deviation ()

500lt0 5

1~~500 10

1~0~100 15

0lt1 gt25

A full correlation was assumed since the JENDL-32 data were obtained from nuclear

model calculations and a strong correlation was expected in such calculations

4) (nd) reaction cross section

The covariances were obtained on the basis of the measurements of LillieI4)

The result is shown in Fig 3

5) (ny) reaction cross section

The covariances were estimated from the measurements of Wtist et al IS) and

Igashira et al 16) The result is shown in Fig 4

6) (np) reaction cross section

The covariances were estimated from the measurements of Borman et al 17gt

DeJuren and StooksberryI8) Seeman and MooreI9) and Martin20) The result is shown

in Fig 5

7) (na) reaction cross section

The covariances were estimated from the following experimental data

Nordborg et al2l) Davis et al 22gt Sick et a1 23gt Divatia et al24) Dickens and

Perey2S) Orphan et a126) and Bair and Haas27)

The result is shown in Fig 6 In the energy region above 7 MeV experimental data

are discrepant with each other

22 Covariance Estimation Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The CASTHY code yielded the covariances of the inelastic scattering cross

section using the KALMAN system The measurements of Nordborg et al21) were

used to deduce the uncertainties in the model parameters

2) Angular distributions for the elastic scattering

In JENDL-32 the angular distributions of elastically scattered neutrons were

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lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

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JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

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lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

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JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

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JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

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lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

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lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

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JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

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JAERI-Research 97-074

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5) Igarasi S and Fukahori T JAERI-1321 (1991)

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IAEA SMR-98 (1970)

8) Kanda Y et al Simultaneous Evaluation of Fission and Capture Cross Sections

and Covariances for Heavy Nuclei Proc Int Conf Nuclear Data for Basic and

Applied Science Santa Fe 1985 p 1567 (1986) Gordon and Breach

9) Rose PF and Dunford CL ENDF-I02 Data Formats and Procedures for the

Evaluated Nuclear Data File ENDF-6 BNL-NCS 44945 (1990)

10) Cierjacks S et al Nucl Instrum Meth~ 185 (1980)

11) Larson DC ORELA Measurements to Meet Fusion Energy Neutron Cross

Section Needs Proc Symp Neutron Cross-Sections from 10 to 50 Me V BNLshy

NCS-51245 p 277 (1980)

12) Brill OD et al Sov Phys Doklady 624 (1961)

13) Oh SY and Shibata K Private communication (1996)

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JAERI-Research 97-074

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27) Bair JK and Haas FX Phys Rev C] 1356 (1973)

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80) Ngoc PN et al Private communication (1980)

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

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88) Fasoli U et al Nucl Phys Al25 227(1969)

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97) Pattenden NJ et al AERE-R-7425 (1973)

98) Schwartz RB et al NBS-MONO-138 (1974)

99) Terrel J and Holm DM Phys Rev102 2031 (1958)

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101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

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103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

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107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

108) Hopkins JC and Gilbert MG Nucl Sci Eng 12 431 (1964)

109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

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112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

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JAERI-Research 97-074

116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

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Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

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122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

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Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

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133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

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lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

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147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

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19881-282 (1988)

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169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

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185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 8: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

Cross section 0 (mb) Standard deviation ()

500lt0 5

1~~500 10

1~0~100 15

0lt1 gt25

A full correlation was assumed since the JENDL-32 data were obtained from nuclear

model calculations and a strong correlation was expected in such calculations

4) (nd) reaction cross section

The covariances were obtained on the basis of the measurements of LillieI4)

The result is shown in Fig 3

5) (ny) reaction cross section

The covariances were estimated from the measurements of Wtist et al IS) and

Igashira et al 16) The result is shown in Fig 4

6) (np) reaction cross section

The covariances were estimated from the measurements of Borman et al 17gt

DeJuren and StooksberryI8) Seeman and MooreI9) and Martin20) The result is shown

in Fig 5

7) (na) reaction cross section

The covariances were estimated from the following experimental data

Nordborg et al2l) Davis et al 22gt Sick et a1 23gt Divatia et al24) Dickens and

Perey2S) Orphan et a126) and Bair and Haas27)

The result is shown in Fig 6 In the energy region above 7 MeV experimental data

are discrepant with each other

22 Covariance Estimation Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The CASTHY code yielded the covariances of the inelastic scattering cross

section using the KALMAN system The measurements of Nordborg et al21) were

used to deduce the uncertainties in the model parameters

2) Angular distributions for the elastic scattering

In JENDL-32 the angular distributions of elastically scattered neutrons were

- 3 shy

~---~~-~---------------------

lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

-4shy

JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

-5shy

lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

-6shy

JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

-7shy

JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

-8shy

JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

-9shy

JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

-10 shy

lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

- 11shy

JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

-12shy

JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

- 13shy

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

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JAERI-Research 97-074

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lAERI-Research 97 -074

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JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 9: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

evaluated in the following way

10-5 eV - 3 MeV 5 MeV - 9 MeV Resonance theory

3MeV-5MeV Measurements28)

9 MeV - 15 MeV Measurements29)

15 MeV - 20 MeV Optical model calculations

The covariances of the 1 st order Legendre coefficient were estimated on the basis of the

same method that had been taken in the JENDL-32 evaluation In the energy region

where the resonance theory was adopted a standard deviation of 10 was assumed for

the neutron width by considering available experimental data and then the covariances

of the Legendre coefficient were calculated by using the law of error propagation The

optical model code ELIESE-3 was used to calculate the covariances above 15 MeV

3 SodiUDt-23

Covariances were obtained for the total inelastic scattering (n2n) (nna)

(nnp) (ny) (np) (n a) reaction cross sections resolved resonance parameters and the

1st order Legendre coefficient for the elastic scattering

31 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 350 keV The

data were taken from the compilation of Mughabghab et al 30) In the present work we

adopted those uncertainties in resonance energy neutron width and capture width

which were recommended by Mughabghab et al However as for the negative

resonance the relative errors of 0 and 1 were assumed for the neutron and capture

widths respectively by considering the reproducibility of the thermal cross sections

32 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the measurements

of Cieljacks et al31) Langsford et al32gt Stoler et al33gt and Larson et a134

) The results

are shown in Figs 7 and 8

-4shy

JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

-5shy

lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

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JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

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JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

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lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

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lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

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JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

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JAERI-Research 97-074

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JAERI-Research 97-074

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103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

104) Ryves TB et al Metrologia14 127 (1978)

105) Ikeda Y et al JAERI-1312 (1988)

106) Li Chi-chou et al INDC(CPR)-16 (1989)

107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

108) Hopkins JC and Gilbert MG Nucl Sci Eng 12 431 (1964)

109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

238 Proc Int Conf Nuclear Physics Berkley 1980 LBL-11118 p243 (1980)

112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

(1962)

115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

- 23shy

JAERI-Research 97-074

116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

(1984)

121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

165 Vol 1 (1967)

122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

131) CorviF et al NEANDC(E) 232U VolllEuratom P5 (1981)

132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

- 24shy

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

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lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

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lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 10: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section

The following measurements were taken into account

Prestwood35) Menlove et al36

) Barral et a137) Maslov et al38

) Araminowicz et

a139) Sigg40

) Shani41 gt Adamski et al42gt and Xu Zhi-Zheng et a143)

Figure 9 shows the JENDL-32 values and their uncertainties In the figure there exist

two groups of measurements above 145 MeV It should be noted that the lower group

was recognized to represent the correct cross sections for this reaction

3) (nY) reaction cross section

In JENDL-32 this reaction cross section was evaluated by using the statistical

model code CASTHY However the parameter values used in the evaluation are no

longer available and our CASTHY calculations could not reproduce the JENDL-32

data Thus in the present work we estimated the covariance of the cross section by

applying the GMA code The following twenty-one data sets were used in fitting

Cocking et al44gt Macklin et al45) Perkin et al46gt Leipunskij et a147gt Kononov et

al48) Booth et a149

) Jowitt et al50) Bame et al 51 gt Lyon et a152

) Meadows et al53)

Macklin et al54gt Rigoleur et al55gt Csikai et a156gt Menlove et a157) Hasan et a158gt

Ryves et al59) Yamamuro et al60

) Holub et a161 gt Sigg40gt and Magnusson et al62)

The result is shown in Fig 10 The correlation obtained is not so strong since there

are few experimental data sets which cover a wide energy range

4) (n p) reaction cross section

The GMA code was applied to estimated the covariances The following

measurements were used

Paul et a163gt Khirana et al64gt Mukjerjee et a165) Williamson66

) Khurana et al67gt

Picard et al68) Mitra et a169gt Bass et al70gt Prasad et al71

) Csikai et al56) Flesch

et al72) PasquarellC3

) Schantal74gt Bartle75) Weigmann et al76

) and Peplink et

al77)

The result is shown in Fig 11 In the low energy region the relative standard

deviation is 2-6 except for the threshold energy (13) The estimated uncertainties

look reasonable in the whole energy region

5) (na) reaction cross section

The GMA code was applied to estimate the covariances The following

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lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

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JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

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JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

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JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

-10 shy

lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

- 11shy

JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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JAERI-Research 97-074

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lAERI-Research 97-074

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- 23shy

JAERI-Research 97-074

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Trans Am Nucl Soc 13 449 (1995)

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Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

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127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

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Harwell 1978 p 1054 (1978)

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132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

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141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

- 24shy

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

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169) Guenther P et al ANllNDM-16 (1975)

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Kiev Vol 2 p119 (1977)

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- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

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180) Barry JF et al J Nucl Energ 18 481 (1964)

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(1976)

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190) Nadolny et al USNDC-9 p170 (1973)

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192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 11: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

measurements were used

Mukherjee et al65) Bizzeti et al78

) Picard et al68gt Bass et al70gt Woelfer et a179)

Fleshi et al72gt Bartle75) Ngoc et al80

) Weigmann et al76) Leich et al8

1) and

Sanchez et al 82)

The result is shown in Fig 12

33 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross section

The statistical model code CAS THY was used to estimate the covariances by

using the KALMAN system The uncertainties in the model parameters were derived

by fitting to the following measurements

Freeman et al83gt Shipley et al84gt Towel et a185) Glazkov et al86

) Chien et al87gt

Fasoli et al88) Pereyet a189gt Coles et al90gt and Schweitzer et al9

t)

2) (nna) and (nnp) reaction cross sections

The statistical model code EGNASH was used to estimate the covariances of the

cross sections The uncertainties in the model parameters were obtained from the

measurements on the (np) (na) (nnp) and (nna) reactions The measurements on

the (np) and (na) reactions mentioned in Sec 32 were taken into account together

with those of Leich et al8 I) for the (nnp) reaction and of Woelfer et al79

) for the (nna)

reaction The standard deviations of the (nna) and (nnp) cross sections are shown in

Figs 13 and 14 respectively

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient were calculated by using

the optical model code ELIESE-3 on the KALMAN system The standard deviation

of the coefficient is shown in Fig 15

4 Natural Iron

A covariance file for natural iron was produced in the present work The

JENDL-32 data for natural iron were made from the isotopic data except the total cross

section which was obtained from experimental data on the natural element The

-6shy

JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

-7shy

JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

-8shy

JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

-9shy

JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

-10 shy

lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

- 11shy

JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

-12shy

JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

- 13shy

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

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JAERI-Research 97-074

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- 24shy

lAERI-Research 97-074

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- 25shy

lAERI-Research 97 -074

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- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 12: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

contribution of minor isotopes e4Pe 57Pe and 58Pe) to the covariance for the natural

element is quite small since the weight for each isotope is the square of the isotopic

abundance Therefore the covariances for the most abundant 56Pe were estimated

except for the total cross section

41 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters for 56Pe are given until 250 keY

with the multi-level Breit-Wigner formula The JENDL-32 evaluation is based on the

analysis by Perey et al92) In the present work the covariances of the resonance

parameters were mainly taken from the same analysis The details are given in a

previous report93)

42 Covariances Based on Measurements

1) Total cross section

There exist a lot of experimental data on elemental iron The GMA code was

applied to estimate the covariances from the measurements of Carlson and Cerbone94)

Cierjacks et al95) Pereyet a196) Pattenden et al97) and Schwartz et a198) Pigures 16

and 17 show the estimated standard deviations Below 3 MeV the uncertainties are

large because of resonance structure

2) (np) reaction cross section

The GMA code was applied to estimate the covariances from the experimental

data on the 56Pe(np) reaction The measurements used are given as follows

Terrel et a199) Bormann et alI)(raquo Santry and ButlerlOl) Liskien and PaulsenI02)

Smith and MeadowsI03) Ryves et al I04) Ikeda et al 105 and Li et al 106

)

Pigure 18 shows the result

43 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering and (ny) reaction cross sections

The CAS THY code was used to estimate the covariances The following

measurements for 56Pe were used to derive the uncertainties in the model parameters

Inelastic scattering

Smith and Guenther07) Hopkins and GilbertI08) Benjamin et al U )9) and Kinney

-7shy

JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

-8shy

JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

-9shy

JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

-10 shy

lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

- 11shy

JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

- 13shy

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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lAERI-Research 97-074

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lAERI-Research 97 -074

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- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 13: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

and PereyllO)

(n y) reaction

Huang et al I1 )) and Allen et aL 112

)

Figure 19 shows the result of the (n 1) reaction on the natural element It is found

from the figure that the JENDL-32 values are much smaller than measured values

above lOMeV since the direct capture was not considered in the evaluation

Therefore the differences between the JENDL-32 cross sections and those calculated

by using a systematics I13gt which reasonably reproduces measured values were given as

the uncertainties above 10 MeV

2) (n2n) (nna) (nnp) (nd) (nt) and (n a) reaction cross sections

The EGNASH code was used to estimated the covariances The covariances of

the model parameters were obtained by considering experimental data on the (n2n) and

(np) reactions The measurements for the (np) reaction on 56Fe were mentioned in

Sect 42 while those for the (n2n) reaction on 56Fe are given as follows

Wenusch and VonachIl4) Corcalciuc et aL 1I5) and Frehaut et aL 1I6

)

Figures 20 and 21 show the standard deviations obtained for the (n2n) and (n a)

reactions on the natural element respectively

3) Angular distributions for the elastic scattering

The ELIESE-3 code was used to estimate the covariances of the pt order

Legendre coefficient for the elastic scattering The uncertainties in the optical model

parameters were obtained by considering the experimental data on the total cross

section mentioned in Sect 42 Figure 22 shows the estimated relative standard

deviation

5 Uranium-235

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nAn)

and (n1) reaction cross sections unresolved resonance parameters average number of

neutrons emitted in fission and the 1st order Legendre coefficient for the elastic

scattering

-8shy

JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

-9shy

JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

-10 shy

lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

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lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

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JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

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JAERI-Research 97-074

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176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 14: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

51 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given in the energy region

below 500 e V while unresolved ones are given in the range from 500 e V to 30 ke V

The resolved resonance parameters in the Reich-Moore type were taken from ENDFIBshy

VI2 However the covariances of the parameters are not available at the Oak Ridge

National Laboratory where the evaluation I 17) for ENDFIB-VI2 was done Therefore

in the present work we gave up making the covariances of the parameters since it was

almost impossible to deduce them independently In the next version JENDL-33 we

will probably adopt the latest resonance parameters obtained by Leal et aI IIS) and their

estimated covariances may be compiled into JENDL-33

The unresolved resonance parameters in JENDL-32 were obtained by fitting to

experimental data on the total capture and fission cross sections with the ASREP9)

code The initial average parameters required as input to the code were taken from the

compilation of Mughbghab 20) In the present work the standard deviations of the

average parameters such as a capture width rY a level spacing D s- and p-wave strength

functions So SI were estimated on the basis of the work of Mughabghab The

uncertainty in the fission width r f was determined form its energy dependence in the

range of 500 e V to 30 keV The relative standard deviations are given as follows

Lry= 5 LD = 10

LSo = 10 LSI =17

Lr3) = 30 Lr4-) = 40 for s-wave

Lr2+) = 40 Lr3+) = 30 forp-wave

Lr4+) =40 Lr5+) = 40 for p-wave

52 Covariances Based on Measurements

The GMA code was applied to estimated the covariances of the cross sections

except the fission cross section

1) Fission cross section

In JENDL-32 the fission cross section was obtained by the simultaneous

evaluationS) in the energy region above 30 ke V Figure 23 shows the standard

deviation and correlation coefficient obtained

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JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

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lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

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JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

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lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

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lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

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JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

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JAERI-Research 97-074

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161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 15: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

2) Total cross section

In the energy region above 30 ke V the covariances were estimated from the

following measurements

Uuley et al 121) Bockhoff et al I22

) Schwartz et al 123gt Green and Mitchell 1 24)

Foster Jr and Glasgow25) Poenitz et al I26

) and Poenitz and Whalen27)

Figures 24 and 25 show the estimated standard deviations

3) (n2n) reaction cross section

There exist two sets of measurements Frehaut et al 128) and Mather et al 129

)

The JENDL-32 evaluation is based on the measurements of Frehaut et al Therefore

the covariances were estimated from the same experimental data A systematic error

of 6 was obtained from Ref 128 and it was considered in the GMA analysis In the

energy region above 14 MeV a relative standard deviation of 50 was assigned since

no measurement is available The result is shown in Fig 26

4) (n3n) and (n4n) reaction cross sections

There are two sets of measurements ie Mather et aL 129) and Veeser and

Arthur130) for the (n3n) reaction while there exists only one set of data measured by

Vesser and Arthur130) for the (n4n) reaction The JENDL-32 evaluation is based on

the measurement of Vesser and Arthur and the covariances were estimated from their

data A systematic error of 5 which came from neutron flux was taken into account

in the GMA analysis

5) (ny) reaction cross section

The covariances were estimated from the measurements of Corvi et al 13l) Gwin

et al 132gt Kononovet al 133) and Hopkins and Diven134

) Error information for each

experiment is given as follows

Corvi et al 131)

Statistical errors are given in the data A systematic error of 4 due to

normalization was considered in the GMA analysis

Gwio et al 132)

Statistical errors were calculated from those for fission and absorption cross

sections A systematic error of 15 was obtained from an uncertainty in the a

values they measured

Kononoy et al 133)

-10 shy

lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

- 11shy

JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

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lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

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JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 16: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

Total errors are given in the data A systematic error of 103 was obtained

from an uncertainty in the a values they measured

Hopkins and Djyen134)

Statistical errors are given in the data A systematic error of 7 was obtained

from the contribution of the 238U contamination in the sample

Relative standard deviations of more than 50 were assigned in the energy region

above 10 MeV where the JENDL-32 evaluation is based on statistical model

calculations since the direct-capture process was not considered in the evaluation

Figure 27 shows the estimated standard deviation

6) A verage number of prompt neutrons

The covariances were estimated from eight sets of measurementsI35-142) Error

information for each experiment is given as follows

Gwin et al 135) 500 ke V-lOMeV

Statistical errors are given in the data A systematic error of 02 was

obtained from Ref 135

Gwin et al 136) 0005 eV - 60 eV

Total and statistical errors are given in the data An average systematic error of

03 was calculated

Gwin et al 137) 500 eV - 11115 MeV

Statistical errors are given in the data A systematic error of 03 was derived

from Ref 137

Gwin et al 138) 50 eV -72 MeV

Statistical errors are given in the data A systematic error of 05 was

assumed

Erehaut et al 139) 1143 MeV - 14656 MeV

Statistical errors are given in the data A systematic error of 03 was

assumed

Frehaut et al 14O) 136 MeV - 28280 MeV

Statistical errors are given in the data A systematic error of 0400 was

assumed

Erehaut and Boldemao141 ) 210 keV -1870 MeV

Statistical errors are given in the data A systematic error of 05 was

- 11shy

JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

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JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

- 13shy

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 17: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

assumed

HmYe142) 170 MeV-489 MeV

Total and statistical errors are given in the data A systematic error of 19

was calculated

Figure 28 shows the estimated standard deviation In the whole energy region the

relative standard deviation is less than 100

7) Average number of delayed neutrons

The covariances were estimated from thirteen sets of measurements143-155)

Error information for each experiment is given as follows

Synetos et al 143) 00253 eV

Total and statistical errors are given in the data A systematic error of 45

was calculated

Besant et al 144) 063 MeV

Statistical errors are given in the data A systematic error of 45 was

assumed

eox45 ) 096 MeV - 398 MeV

Total errors are given in the data A systematic error of 5 was assumed

Eyans et al 146) 005 MeV - 67 MeV

Total errors are given in the data A systematic error of 5 was assumed

Clifford et al 147) 063 MeV

Total errors are given in the data A systematic error of 5 was assumed

Conant et al 148) 00253 eV

Total errors are given in the data A systematic error of 5 was assumed

Masters et al149) 31149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin150) 141 149 MeV

Total errors are given in the data A systematic error of 5 was assumed

Maksyutenko et aJ 151) 00253 eV 24 MeV 33 MeV

Total errors are given in the data A systematic error of 5 was assumed

Keepin et al 152) 00253 eV 145 MeV

Total errors are given in the data A systematic error of 5 was assumed

Rose et aI 153) 1 MeV

-12shy

JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

- 13shy

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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JAERI-Research 97-074

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

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JAERI-Research 97-074

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- 24shy

lAERI-Research 97-074

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- 25shy

lAERI-Research 97 -074

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- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 18: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

Total errors are given in the data A systematic error of 5 was assumed

Brunson et al 154) 00253 eV 029 MeV

Total errors are given in the data A systematic error of 5 was assumed

Snell et al 155) 00253 e V

Total errors are given in the data A systematic error of 5 was assumed

Figure 29 shows the estimated standard deviation

53 Covariances Based on Nuclear Model Calculations

The covariances of the inelastic scattering cross sections and the 1st order

Legendre coefficient for the elastic scattering were obtained from statistical and optical

model calculations on the KALMAN system As for the Legendre coefficient we

used the experimental data on the total cross section mentioned in Sec 52 to derive the

covariances of the optical model parameters On the other hand the following

measurements were used for the inelastic scattering

Batchelor and Wyld156gt DrakeI57) Knitter et al 158gt and Smith and GuentherI59)

Figure 30 shows the estimated standard deviation of the 1 st order Legendre coefficient

6 Uranium-238

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (nyen)

and fission cross sections resolved and unresolved resonance parameters and the 1 st

order Legendre coefficient for the elastic angular distribution

61 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 10 keY with the

multi-level Breit-Wigner formula The standard deviations of the parameters are

based on the values obtained by Olsen et al I60]61) and Moxon et al 162)

Unresolved resonance parameters are given in the energy region from 10 keY to

150 keY Uncertainties in an average level spacing D neutron strength functions So

SI S2 and an average capture width ry were deduced from the energy dependence of

these parameters calculated with the ASREP code

- 13shy

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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lAERI-Research 97-074

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- 23shy

JAERI-Research 97-074

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- 24shy

lAERI-Research 97-074

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- 25shy

lAERI-Research 97 -074

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- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 19: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

~D=5

62 Covariances Based on Measurements

1) Total cross section

The GMA code was applied to estimate the covariances from the following

measurements

Whalen and Smithl63)

Statistical errors are given in the data A systematic error of 3 was assumed

Poenitz et a1 126)

Total and statistical errors are given in the data A systematic error of 04 was

deduced

Tsubone et al I64)

Total errors are given in the data A systematic error of 22 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Bratenabal et al 165)

Total errors are given in the data A systematic error of 0500 is given in Ref

165

Peterson et al 166)

Total errors are given in the data A systematic error of 05 is given in Ref

166

Figure 31 shows the estimated standard deviations

2) (n2n) and (n3n) reaction cross sections

In JENDL-32 the (n2n) reaction cross section was evaluated from the

measurements of Veeser and Arthur13O) Frehaut et aI 128

) and Karius et al 167) The

covariances of the cross section were obtained from these data by using the splineshy

function fitting Error information for each data set is given as follows

Vesser and Arthue30)

Total errors are given in the data A systematic error of 35 was assumed

Frehaut et a1 128)

Total errors are given in the data A systematic error of 35 was assumed

-14 shy

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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- 20shy

JAERI-Research 97-074

22) Davis EA et al Nucl Phys 48 169 (1963)

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29) Glendinning SG et al Nucl Sci Eng 82 393 (1982)

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36) Menlove HO et al Phys Rev 163 1308 (1967)

37) Barrall RC et al AFWL-TR-68-134 (1969)

38) Malov GN et al Yadernye Konstanty 250 (1972)

39) Aramnowicz et al INR-1464 14 (1973)

40) Sigg RA Private communication (1976)

41) Shani G INIS-MF-3663 83 (1976)

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43) Xu Zhi-zheng et al Proc Int Conf Nuclear Data for Science and Technology

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49) Booth R et al Phys Rev 112226 (1958)

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51) Bame Jr et al Phys Rev 113256 (1959)

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52) Lyon WS et al Phys Rev 114 1619 (1959)

53) Meadows JW et al Nucl Sci Eng 9 132 (1961)

54) Macklin RL et al Phys Rev 1292695 (1963)

55) Rigoleur et al J Nucl Energy 2067 (1966)

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79) Woelfer G et al Z Physik~ 75(1966)

80) Ngoc PN et al Private communication (1980)

81) Leich DA et al Private communication (1985)

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83) Freeman JM et al Nucl Phys 2 181(1958)

84) Shipley EN et al Phys Rev 115 122(1959)

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

87) Chien JP et al Nucl Sci Eng 26 500 (1966)

88) Fasoli U et al Nucl Phys Al25 227(1969)

89) Perey FG et alORNL-4518 (1970)

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p530 (1979) Pergamon Press

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96) Perey FG et al ORNL-4823 (1972)

97) Pattenden NJ et al AERE-R-7425 (1973)

98) Schwartz RB et al NBS-MONO-138 (1974)

99) Terrel J and Holm DM Phys Rev102 2031 (1958)

100) Bormann M et al Z Phys 166477 (1962)

101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

102) Liskien H and Paulsen A Nukleonik8 315 (1966)

103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

104) Ryves TB et al Metrologia14 127 (1978)

105) Ikeda Y et al JAERI-1312 (1988)

106) Li Chi-chou et al INDC(CPR)-16 (1989)

107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

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109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

238 Proc Int Conf Nuclear Physics Berkley 1980 LBL-11118 p243 (1980)

112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

(1962)

115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

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116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

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121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

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122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

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133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

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142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

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147) Clifford DA PhD Thesis Imperial College London (1972)

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149) Masters CF et al Nucl Sci Eng36 202 (1969)

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151) Maksyutenko BP JETP8 565 (1959)

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1979 p 677 (1980)

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19881-282 (1988)

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164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

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169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 20: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

Karius et al 167)

Partial errors are given in the data

The (n3n) reaction cross section in JENDL-32 is based on the measurements of

Veeser and Althur130) The covariances of the cross section was obtained in the same

manner as the (n2n) reaction

Figures 32 and 33 shows the standard deviations of the (n2n) and (n3n) cross

sections respectively

3) Fission cross section

The covariances were obtained from the simultaneous evaluation8gt and the result

is shown in Fig 34

63 Covariances Based on Nuclear Model Calculations

1) Inelastic scattering cross sections

In JENDL-32 the cross sections are given for 33 excited levels among which

the 28th to 33rd levels were created so as to reproduce available experimental data on

neutron emission spectra The covariances of the cross sections for the real 27 levels

were obtained from the coupled-channel and statistical model calculations on the

KALMAN system The uncertainties in the model parameters were derived from the

measurementsI68-173) for the 1st and 2nd excited states A standard deviation of 2000 was

assumed for the six pseudo levels and the continuum level

2) (ny) reaction cross section

The CASTHY code was used to estimate the covariances in the energy region

from 150 ke V to 2 Me V The uncertainties in the model parameters were derived by

fitting to the following experimental data

Frickel74gt Drake et al 175) Lindnerl76gt Poenitz l77) Diven et aI 178) McDaniels et

al 179) Barry et al 180) Perkin et al 18

1) Brodal82gt Huang et al 183) Panitkin et al I84)

Davletshin et al 185) Buleeva et al I86) and Kazakov et al 187)

Above 2 MeV the direct-semidirect modelJ88) was used to estimate the covariances and

the result was combined with those obtained by the CASHY calculations Figure 35

shows the estimated standard deviation

3) Angular distributions for the elastic scattering

The covariances of the 1 st order Legendre coefficient for the elastic scattering

- 15

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 21: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

was obtained by using the ECIS code on the KALMAN system The uncertainties in

the optical model parameters were estimated by fitting to the measurements on the total

cross section mentioned in Sect 62 Figure 36 shows the estinlated standard

deviation

7 Plutonium-239

Covariances were obtained for the total inelastic scattering (n2n) (n3n) (n4n)

(ny) and fission cross sections resolved and unresolved resonance parameters and the

1st order Legendre coefficient for the elastic angular distribution

7 1 Covariances of Resonance Parameters

In JENDL-32 resolved resonance parameters are given below 25 ke V with the

Reich-Moore formula The covariances of the parameters were obtained from the

analysis of Derrienl89) in the energy region from 1 keY to 25 keY No covariance was

given below 1 ke V since the data were no longer available at ORNL where the

evaluation of the parameters had been performed

The covariances of the unresolved resonance parameters which are given in the

range of 25 ke V to 30 ke V was taken from the previous work93)

~D =5 ~ry=1

~SO =10 ~SI =15

~rf (0+ 1+) =15 ~rf (0- 1-2-) =20

where the meaning of the symbols is the same as that in Sect 61

72 Covariances Based on Measurements

1) Total cross section

In the energy region from 30 ke V to 7 Me V the covariances were estimated on

the basis of the optical model calculations which are described in Sect 73 Above 7

MeV the GMA code was used to obtain the covariances from the following

measurements

Schwartz et al 123)

- 16shy

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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- 22shy

lAERI-Research 97-074

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- 23shy

JAERI-Research 97-074

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- 24shy

lAERI-Research 97-074

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- 25shy

lAERI-Research 97 -074

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- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 22: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

Statistical error is given in the data A systematic error of 11 was deduced

Foster Jr and Glasgowl25)

Total errors are given in the data A systematic error of 05 was deduced

Nadolny et al l90)

Statistical errors are given in the data A systematic error of 1 was deduced

Poenitz and Whalen 127)

Total errors are given in data A systematic error of 093 was deduced

The estimated standard deviation is shown in Fig 37

2) (n2n) reaction cross section

The GMA code was applied to estimate the covariances of the cross section from

the measurements of Frehaut et al 191) A systematic error of 9 which was deduced in

Ref 191 was put into the code The result is shown in Fig 38

3) (n3n) and (n4n) reaction cross sections

The JENDL-32 evaluation is based on nuclear model calculations However

the parameters required as input to the model code are no longer available Moreover

experimental data on these reactions are very scarce and it is impossible to determine

the covariances experimentally Therefore we used the rule of OhI3) which was applied

to the 160(nnp) and 160(nno) reactions with a full correlation

4) (ny) reaction cross section

The GMA code was used to estimated the covariances in the energy region from

30 keY to 1 MeV The measurements used are given as follows

Spivak et al 192gt Hopkins and Divenl34gt and Kononov et al 193)

The variance obtained at 1 Me V was used without any correlation up to 8 Me V In the

energy region above 8 MeV a relative standard deviation of 100 was assumed since

the direct capture was not considered in the JENDL-32 evaluation Figure 39 shows

the estimated standard deviations

5) Fission cross section

The covariances of the fission cross section was obtained by the simultaneous

evaluation8gt and the result is shown in Fig 40

73 Covariances Based on Nuclear Model Calculations

1) Total cross section

- 17shy

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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- 20shy

JAERI-Research 97-074

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21shy

JAERI-Research 97-074

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57) Menlove HO et al Phys Revl63 1299 (1967)

58) Hasan SS et al Nuovo CimentoB58 402 (1968)

59) Ryves TBet alJ Nucl Energy 24419(1970)

60) Yamamuro N et al Nucl Sci Eng 41 445(1970)

61) Holub E et alLNS-4-72 (1972)

62) Magnusson G et al Physica Scripta 21 121(1980)

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64) Khurana CS et al Proc Symp on Low Energy Nucl Phys Waltair 1960

p297(1960)

65) Mukherjee SK et al Proc Phys Soc 77 508(1961)

66) Williamson CF Phys Rev 122 1877(1961)

67) Khurana CS et al Nucl Phys 62 153 (1965)

68) Picard J et al Nucl Phys 63673 (1965)

69) Mitra B et al Nucl Phys8 157 (1966)

70) Bass R et al EANDC(E)-66 p64 (1966)

71) Prasad R et al Nucl Phys85 476 (1966)

72) Flesch F et al Oesterr Akd Wiss 116 45 (1967)

73) Pasquarelli A Nucl Phys A23 218 (1967)

74) Schantl W Private communication (1970)

75) Bartle CM Nucl Iostrum Methods l24 547 (1975)

76) Weigmann H et alProc lot Conf on Nucl Data and Technol Antwerp 1982

p814(1982)

77) Pepelink R et al NEANDC(E)-262U Vol V p32(1985)

78) Bizzeti PG et al Nucl Phys36 38(1962)

79) Woelfer G et al Z Physik~ 75(1966)

80) Ngoc PN et al Private communication (1980)

81) Leich DA et al Private communication (1985)

82) Sanchez et al NEANDC(OR)-140 p 8 (1974)

83) Freeman JM et al Nucl Phys 2 181(1958)

84) Shipley EN et al Phys Rev 115 122(1959)

85) Towel JH et al Nucl Phys32 610(1962)

- 22shy

lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

87) Chien JP et al Nucl Sci Eng 26 500 (1966)

88) Fasoli U et al Nucl Phys Al25 227(1969)

89) Perey FG et alORNL-4518 (1970)

90) Coles RE et alAWRE-O-0371 (1971)

91) Schweitzer Th et al Private Communication(1978)

92) Perey FG et al Recent Results for 58Ni and 56Fe at ORELA Proc Specialists

Meeting on Neutron Data of Structural Materials for Fast Reactors Geel 1977

p530 (1979) Pergamon Press

93) Nakagawa T and Shibata K Estimation of Uncertainties in Resonance

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Japanese]

94) Carlson AD and Cerbone RJ Nucl Sci Eng 42 28 (1970)

95) Cierjacks S et al KFK-1000 (1969)

96) Perey FG et al ORNL-4823 (1972)

97) Pattenden NJ et al AERE-R-7425 (1973)

98) Schwartz RB et al NBS-MONO-138 (1974)

99) Terrel J and Holm DM Phys Rev102 2031 (1958)

100) Bormann M et al Z Phys 166477 (1962)

101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

102) Liskien H and Paulsen A Nukleonik8 315 (1966)

103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

104) Ryves TB et al Metrologia14 127 (1978)

105) Ikeda Y et al JAERI-1312 (1988)

106) Li Chi-chou et al INDC(CPR)-16 (1989)

107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

108) Hopkins JC and Gilbert MG Nucl Sci Eng 12 431 (1964)

109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

238 Proc Int Conf Nuclear Physics Berkley 1980 LBL-11118 p243 (1980)

112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

(1962)

115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

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JAERI-Research 97-074

116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

(1984)

121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

165 Vol 1 (1967)

122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

131) CorviF et al NEANDC(E) 232U VolllEuratom P5 (1981)

132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

- 24shy

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 23: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

The optical model code ELIESE-3 was used to estimate the covariances in the

energy region from 30 ke V to 7 Me V The uncertainties in the optical model

parameters were obtained by fitting to the total cross section data mentioned in Sect 72

and to the measurements of Poenitz et al 126) Figure 41 shows the estimated result

2) Inelastic scattering cross section

The CASTHY code yielded the covariances the cross sections The

uncertainties in the model parameters were obtained by fitting to the measurements of

7thHaouat et al 170) For the 1 st to 5th and 9th levels a standard deviation of 20 was

assumed with a full correlation in the energy region above 4 MeV since the cross

sections for these levels were evaluated with the coupled-channel model in JENDL-32

and thus a strong correlation was expected

3) Angular distributions for the elastic scattering

The ECIS code was used to estimate the covariances of the 1 st order Legendre

coefficient Figure 42 shows the estimated standard deviation

8 Concluding Remarks

Covariances of nuclear data were estimated for 160 23Na Fe 235U 238U and 239pU

contained in JENDL-32 The quantities of which covariances were obtained are cross

sections resolved and unresolved resonance parameters and the 1 st order Legendre

coefficient for the elastic scattering The uncertainty in the Legendre coefficient was

estimated in order to calculate an uncertainty in an average cosine of elastic-scattering

angles As for 235U we obtained the covariances of the average number of prompt and

delayed neutrons emitted in fission

In covariance estimation we used the same methodology that had been taken in

the JENDL-32 evaluation in order to keep a consistency between mean values and their

covariances The covariances of fission cross sections were taken from the

simultaneous evaluation which had been performed in the JENDL-32 evaluation

The results obtained were compiled in the ENDF-6 format and will be put into

the JENDL-32 Covariance File which is one of the JENDL special purpose files

managed by the JAERI Nuclear Data Center The data are also used in making the

- 18shy

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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lAERI-Research 97-074

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JAERI-Research 97-074

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- 24shy

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- 25shy

lAERI-Research 97 -074

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- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 24: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

integrated group cross-section library promoted by the PNC

Acknowledgment

The authors would like to thank Dr Wakabayashi and Dr Ishikawa of the PNC

for supporting this work They are also grateful to the members of the Working Group

on Covariance Estimation in the Japanese Nuclear Data Committee for their valuable

comments on this work

- 19shy

JAERI-Research 97-074

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JAERI-Research 97-074

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21shy

JAERI-Research 97-074

52) Lyon WS et al Phys Rev 114 1619 (1959)

53) Meadows JW et al Nucl Sci Eng 9 132 (1961)

54) Macklin RL et al Phys Rev 1292695 (1963)

55) Rigoleur et al J Nucl Energy 2067 (1966)

56) Csikai J et al Nucl Phys A25 229 (1967)

57) Menlove HO et al Phys Revl63 1299 (1967)

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60) Yamamuro N et al Nucl Sci Eng 41 445(1970)

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p297(1960)

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67) Khurana CS et al Nucl Phys 62 153 (1965)

68) Picard J et al Nucl Phys 63673 (1965)

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73) Pasquarelli A Nucl Phys A23 218 (1967)

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75) Bartle CM Nucl Iostrum Methods l24 547 (1975)

76) Weigmann H et alProc lot Conf on Nucl Data and Technol Antwerp 1982

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77) Pepelink R et al NEANDC(E)-262U Vol V p32(1985)

78) Bizzeti PG et al Nucl Phys36 38(1962)

79) Woelfer G et al Z Physik~ 75(1966)

80) Ngoc PN et al Private communication (1980)

81) Leich DA et al Private communication (1985)

82) Sanchez et al NEANDC(OR)-140 p 8 (1974)

83) Freeman JM et al Nucl Phys 2 181(1958)

84) Shipley EN et al Phys Rev 115 122(1959)

85) Towel JH et al Nucl Phys32 610(1962)

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

87) Chien JP et al Nucl Sci Eng 26 500 (1966)

88) Fasoli U et al Nucl Phys Al25 227(1969)

89) Perey FG et alORNL-4518 (1970)

90) Coles RE et alAWRE-O-0371 (1971)

91) Schweitzer Th et al Private Communication(1978)

92) Perey FG et al Recent Results for 58Ni and 56Fe at ORELA Proc Specialists

Meeting on Neutron Data of Structural Materials for Fast Reactors Geel 1977

p530 (1979) Pergamon Press

93) Nakagawa T and Shibata K Estimation of Uncertainties in Resonance

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Japanese]

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95) Cierjacks S et al KFK-1000 (1969)

96) Perey FG et al ORNL-4823 (1972)

97) Pattenden NJ et al AERE-R-7425 (1973)

98) Schwartz RB et al NBS-MONO-138 (1974)

99) Terrel J and Holm DM Phys Rev102 2031 (1958)

100) Bormann M et al Z Phys 166477 (1962)

101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

102) Liskien H and Paulsen A Nukleonik8 315 (1966)

103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

104) Ryves TB et al Metrologia14 127 (1978)

105) Ikeda Y et al JAERI-1312 (1988)

106) Li Chi-chou et al INDC(CPR)-16 (1989)

107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

108) Hopkins JC and Gilbert MG Nucl Sci Eng 12 431 (1964)

109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

238 Proc Int Conf Nuclear Physics Berkley 1980 LBL-11118 p243 (1980)

112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

(1962)

115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

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116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

(1984)

121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

165 Vol 1 (1967)

122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

131) CorviF et al NEANDC(E) 232U VolllEuratom P5 (1981)

132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

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142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

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157) Drake DM Nucl Phys A133 108 (1969)

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1979 p 677 (1980)

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19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 25: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

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101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

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- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

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193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 26: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

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JAERI-Research 97-074

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- 22shy

lAERI-Research 97-074

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115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

- 23shy

JAERI-Research 97-074

116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

(1984)

121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

165 Vol 1 (1967)

122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

131) CorviF et al NEANDC(E) 232U VolllEuratom P5 (1981)

132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

- 24shy

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 27: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

52) Lyon WS et al Phys Rev 114 1619 (1959)

53) Meadows JW et al Nucl Sci Eng 9 132 (1961)

54) Macklin RL et al Phys Rev 1292695 (1963)

55) Rigoleur et al J Nucl Energy 2067 (1966)

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58) Hasan SS et al Nuovo CimentoB58 402 (1968)

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73) Pasquarelli A Nucl Phys A23 218 (1967)

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77) Pepelink R et al NEANDC(E)-262U Vol V p32(1985)

78) Bizzeti PG et al Nucl Phys36 38(1962)

79) Woelfer G et al Z Physik~ 75(1966)

80) Ngoc PN et al Private communication (1980)

81) Leich DA et al Private communication (1985)

82) Sanchez et al NEANDC(OR)-140 p 8 (1974)

83) Freeman JM et al Nucl Phys 2 181(1958)

84) Shipley EN et al Phys Rev 115 122(1959)

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lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

87) Chien JP et al Nucl Sci Eng 26 500 (1966)

88) Fasoli U et al Nucl Phys Al25 227(1969)

89) Perey FG et alORNL-4518 (1970)

90) Coles RE et alAWRE-O-0371 (1971)

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92) Perey FG et al Recent Results for 58Ni and 56Fe at ORELA Proc Specialists

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p530 (1979) Pergamon Press

93) Nakagawa T and Shibata K Estimation of Uncertainties in Resonance

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94) Carlson AD and Cerbone RJ Nucl Sci Eng 42 28 (1970)

95) Cierjacks S et al KFK-1000 (1969)

96) Perey FG et al ORNL-4823 (1972)

97) Pattenden NJ et al AERE-R-7425 (1973)

98) Schwartz RB et al NBS-MONO-138 (1974)

99) Terrel J and Holm DM Phys Rev102 2031 (1958)

100) Bormann M et al Z Phys 166477 (1962)

101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

102) Liskien H and Paulsen A Nukleonik8 315 (1966)

103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

104) Ryves TB et al Metrologia14 127 (1978)

105) Ikeda Y et al JAERI-1312 (1988)

106) Li Chi-chou et al INDC(CPR)-16 (1989)

107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

108) Hopkins JC and Gilbert MG Nucl Sci Eng 12 431 (1964)

109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

238 Proc Int Conf Nuclear Physics Berkley 1980 LBL-11118 p243 (1980)

112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

(1962)

115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

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JAERI-Research 97-074

116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

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121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

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122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

131) CorviF et al NEANDC(E) 232U VolllEuratom P5 (1981)

132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

- 24shy

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 28: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

86) Glazkov NP et al Atomnaya Energiya lS 416(1963)

87) Chien JP et al Nucl Sci Eng 26 500 (1966)

88) Fasoli U et al Nucl Phys Al25 227(1969)

89) Perey FG et alORNL-4518 (1970)

90) Coles RE et alAWRE-O-0371 (1971)

91) Schweitzer Th et al Private Communication(1978)

92) Perey FG et al Recent Results for 58Ni and 56Fe at ORELA Proc Specialists

Meeting on Neutron Data of Structural Materials for Fast Reactors Geel 1977

p530 (1979) Pergamon Press

93) Nakagawa T and Shibata K Estimation of Uncertainties in Resonance

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Japanese]

94) Carlson AD and Cerbone RJ Nucl Sci Eng 42 28 (1970)

95) Cierjacks S et al KFK-1000 (1969)

96) Perey FG et al ORNL-4823 (1972)

97) Pattenden NJ et al AERE-R-7425 (1973)

98) Schwartz RB et al NBS-MONO-138 (1974)

99) Terrel J and Holm DM Phys Rev102 2031 (1958)

100) Bormann M et al Z Phys 166477 (1962)

101) Santry DC and Butler JP Can J Phys 42 1030 (1964)

102) Liskien H and Paulsen A Nukleonik8 315 (1966)

103) Smith DL and Meadows JW Nucl Sci Eng 58 314 (1975)

104) Ryves TB et al Metrologia14 127 (1978)

105) Ikeda Y et al JAERI-1312 (1988)

106) Li Chi-chou et al INDC(CPR)-16 (1989)

107) Smith A and Guenther P Nucl Sci Eng TI 186 (1980)

108) Hopkins JC and Gilbert MG Nucl Sci Eng 12 431 (1964)

109) Benjamin RW et al Nucl Phys 79241 (1966)

110) Kinney WE and Perey FG Nucl Sci Eng 63 418 (1977)

111) Huang Zheng-de et al Radiative Capture of 142 MeV Neutron by Fe-56 and Ushy

238 Proc Int Conf Nuclear Physics Berkley 1980 LBL-11118 p243 (1980)

112) Allen BJ et al Nucl Phys A269 408 (1976)

113) Benzi V and Reffo G CCDN-NWlO (1969)

114) Wenusch R and Vonach H Oesterr Akad Wiss Math+Naturw Anzeiger 22 1

(1962)

115) Corcalciuc V et al Yademaya Fizika 20 1096 (1974)

- 23shy

JAERI-Research 97-074

116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

(1984)

121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

165 Vol 1 (1967)

122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

131) CorviF et al NEANDC(E) 232U VolllEuratom P5 (1981)

132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

- 24shy

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 29: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

116) Frehaut J et al Private Communication (1980)

117) Leal LC et al Nucl Sci Eng102 1 (1991)

118) Leal LC et al Reevaluation of the 235U Cross Sections for ENDFIB-VI

Trans Am Nucl Soc 13 449 (1995)

119) Kikuchi Y ASREP unpublished

120) Mughabghab SF Neutron Cross Sections Vol 1 Neutron Resonance

Parameters and Thermal Cross Sections Part B Z=61-1 00 Academic Press

(1984)

121) Uttley CA et al Neutron Strength Function Measurements in the Medium and

Heavy Nuclei Proc First IAEA Conf Nuclear Data for Reactors Paris 1966 p

165 Vol 1 (1967)

122) BockhoffKH et al J Nucl Energ 26 91 (1972)

123) Schwartz RB et al Nucl Sci Eng 54 322 (1974)

124) Green L and Mitchell J A Total Cross Section Measurements with a 252Cf

Time of Flight Spectrometer WAPD-TM-I073 (1973)

125) Foster Jr DG and Glasgow DW Phys Rev Q 576 (1971)

126) Poenitz WP et al Nucl Sci Eng 18333 (1981)

127) Poenitz WP and Whalen JF Neutron Total Cross Section Measurements in the

Energy Region from 47 keV to 20 MeV ANL-NDM-80 (1983)

128) Frehaut J et al Nucl Sci Eng 14 29 (1980)

129) MatherDS et al A WRE Report No 07272 (1972)

130) VeeserLR and ArthurED Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p 1054 (1978)

131) CorviF et al NEANDC(E) 232U VolllEuratom P5 (1981)

132) Gwin R et al Nucl Sci Eng52 79 (1976)

133) Kononov VN et al Atomnaya Energiya8 82 (1975)

134) Hopkins JC and Diven BC Nucl Sci Eng 12 169 (1962)

135) Gwin R et al Nucl Sci Eng 24 365 (1986)

136) Gwin R et al Nucl Sci Eng 81 381 (1984)

137) Gwin R et al ORNL-TM-7148 (1980)

138) Gwin R et al ORNL-TM-6246 (1978)

139) Frehaut J et al Proc Int Conf Nuclear Data for Science and Technology

Antwerp 1982 p78 (1982)

140) Frehaut J et al Private communication (1980)

141) Frehaut J and Boldeman J W Proc Int Conf Neutron Physics and Nuclear Data

Harwell 1978 p421 (1978)

- 24shy

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

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174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

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185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

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187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

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192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 30: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

142) Howe RE Nucl Sci Eng 86 157 (1984)

143) Synetos S and Williams JG INDC(NDS)-107 P183 (1979)

144) Besant CB et al BNES16 161 (1977)

145) Cox SA ANllNDM-5 (1974)

146) Evans AE and Thorpe MM Nucl Sci Eng50 80 (1973)

147) Clifford DA PhD Thesis Imperial College London (1972)

148) Conant JF and Palmedo PF Nucl Sci Eng 44 173 (1971)

149) Masters CF et al Nucl Sci Eng36 202 (1969)

150) Keepin GR LA-4320 (1969)

151) Maksyutenko BP JETP8 565 (1959)

152) Keepin GR et al J Nucl Ener 6 1 (1957)

153) Rose H and Smith RD J Nucl Ener 4 141 (1957)

154) Brunson GS et al Nucl Sci Eng 1 174 (1956)

155) Snell et al quoted by RJ Tuttle (INDC(NDS)-107 P29 (1979))

156) Batchelor R and Wyld K AWRE-O-5569 (1969)

157) Drake DM Nucl Phys A133 108 (1969)

158) Knitter H-H Z Phys 251 108 (1972)

159) Smith AB and Guenther PT ANllNDM-63 (1982)

160) Olsen DK et al Nucl Sci Eng 62202 (1979)

161) Olsen DK et al Proc Int Conf Nuclear Cross Sections for Technol Knoxville

1979 p 677 (1980)

162) Moxon MC et al Proc 1988 Int Reactor Physics Conference Jackson Hole

19881-282 (1988)

163) Whalen JF and Smith AB ANL-7710 (1971)

164) Tsubone I et al Nucl Sci Eng 88 579 (1984)

165) Bratenahal A et al Phys Rev llQ 927 (1958)

166) Peterson JM et al Phys Rev 120521 (1960)

167) Krius H et al J Phys G5 5 715 (1979)

168) Beghian LE et al Nucl Sci Eng 62 191 (1979)

169) Guenther P et al ANllNDM-16 (1975)

170) Haouat G et al Nucl Sci Eng81 491 (1982)

171) Smith A Nucl Phys 41 633 (1963)

172) Tsang FY and Brugger RM Nucl Sci Eng 65 70 (1978)

173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics

Kiev Vol 2 p119 (1977)

174) Fricke MP Proc Third Conf Neutron Cross-Section and Technology Knoxville

- 25shy

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 31: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97 -074

1971 Vol 1 p252 (1971)

175) Drake D et al Phys Lett B16 557 (1971)

176) Lindner M Nucl Sci Eng 52381 (1976)

177) Poenitz WP Nucl Sci Eng 5]300 (1975)

178) Diven BC et al Phys Rev12Q 556 (1960)

179) McDaniels DK et al Nucl Phys A184 88(1982)

180) Barry JF et al J Nucl Energ 18 481 (1964)

181) Perkin JL et al Proc Phys Soc 12505 (1958)

182) Broda BR-574 (1945)

183) Huang Z et al LBL-11118 p 243 (1980)

184) Panitkin JuG and Tolstikov VA Atomnaja Energija33 782 (1972)

185) Dabletshin AN et al Proc Third All Union Conf Neutron Physics Kiev 4 109

(1976)

186) Buleeva LE et al Atomnaja Energija 65 348 (1988)

187) Kazakov LE et al Jadernye Konstanty3 37 (1986)

188) Clement CF et al Nucl Phys 66 273 (1965)

189) Derrien H J Nucl Sci Technol 30 845 (1993)

190) Nadolny et al USNDC-9 p170 (1973)

191) Frehaut J et al CEA-N-2500 (1986)

192) Spivak PE et al Atomnaya Energiya 1 21 (1956)

193) Kononov VN et al FEI-274 (1971)

- 26shy

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 32: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI -Research 97 -07 4

Total Cross Section of 160 10------~~--~--~~--~

c o +- () Q)

CJ)

en en o () ~

1

o

o

GMA fit 80 Cierjacks+ 80 Larson

4 6 8 10

Neutron Energy (MeV)

Fig 1 Total cross section of 160 below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 27shy

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 33: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

--

lAERI-Research 97-074

Total Cross Section of 160

-

0 -

C 0

u CD

Cf)

en en 0 () ~

GMA fit o 80 Cierjacks+ o 80 Larson

1

12 16

Neutron Energy (MeV)

Fig 2 Total cross section of 160 above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-28shy

20

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 34: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

0-16(N D)

en C L C

c

c

~

bull I -

-~-~-~----~~~--~~~-----r-------------_

lt rmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotrmiddotmiddotmiddotmiddot ~ ----- ~ --

flO ~

l

I I I

JENDL-32 JENDl-3 2-DEL TA JENDL-3 2tOEL TA

o ABLILLIE

-I

-

0 Co

gttTl 00

Q) 10-5 ~ ~CI) (II

t) ~ (i10 en r

en 0

-J L bU -J f

10-8

100 150 200

Neutron Energy (MeV)

Fig 3 (nd) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 35: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

- - - - shy

~

----shy- ~-

~ - -

1 0 -8 ft I 1 I I io 71 11

10-4

U)

c shya

c 10-5

c 0

u CD

en 10-6 Col) 0

U)I U)

0 shy

cgt

10-7

110 (n Y ) iI I -

I- --~ ) shytTle

~ G ~ rJENDL-32 00 95 IGASHIRA+ --l

b 71 ALLEN+ --l jgtreg 79 WUEST+

Neutron Energy ( eV )

Fig 4 (ny) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 36: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

IIC (n p ) 01001~----~----~~--~----~r_----_----r-----T-----~----~----I

t JENDL-32

0 EBPAUL+ reg HCMARTIN

11111 A JADE JUREN+ ~ JADE JUREN+

bull KWSEEMAN+ UJ

I r JKANTELE+c 0 J KANTELE+- I J KANTELE+C I

0 0 J KANTELE+ I BMITRA+II I EI RPRASAD+c I0 MBORMANN+ gtI tTl0050 WSCHANTL 0

MSCHMIDT-HOENDW+ -0 ~ (ljM L SANCHEZ+ rnCD (lj

c) U) ~ r

UJ UJ 0 0 -)

b shy -)c) j

OOOO~I--------------------~~----~-------L------~------~----~~------------~100 150 200

Neutron Energy (MeV)

Fig 5 (np) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 37: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

0-16(N A) 10 1

Fig 6 (nu) reaction cross section of 160 The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 38: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

Total Cross Section of 23Na

c o-shy u (])

C)

en en o 3

o

- GMA fit o 65 Langsford+ [] 69 Cierjacks+ o 70 Clement+ A 76 Larson+

shy

2 4 6 8 10 Neutron Energy (MeV)

Fig 7 Total cross section of 23Na below 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 33shy

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 39: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

__ _ --~~t---~---

lAERI-Research 97-074

Total Cross Section of 23Na

- GMA fit o 65 Langsford+

CJ 69 Cierjacks+c o 70 Clement+c a 76 Larson+0

() Q) 2

()

----- -~

1_--shyen en 0 ~-- ~

(J ~

10 12 14 16 18 20 Neutron Energy (MeV)

Fig 8 Total cross section of 23Na above 10 MeV The solid line stands for the best estimate and the dashed ones standard deviations

-34shy

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 40: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

I

NA-23(N 2N) 10deg

10-1 en c t c

c

c 0

~

~ 2

I I I I

~ 1 - _ I ~ I II tff IY~- I ~ I bullbull---t--- --------

- ___ __ bull A

T middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotl

EVALUATED MAT NO EVALUATED-DELTA MAT NO EVALpATED DELTA MAT NO

e RJPRESTWOOD 55 reg H LI SKIENt 65 A JPICARDt 65

bull HOMENLOVEt 67

bull

I

RCBARRALLt 69 ~ GNMASLOVt 72m

- 11

t

~

I~ ~

I

AADAMt 72 0 AADAMt 72

GSHANI 76 ~ JARAMINOWICZ 73 o G RASIGG 76

0 L HANNAPELt 79 ltgt LADAMSKlt 80 Y IKEDA 88

bull XU ZHI-ZHENGt 91 I I I I I

-

1

gttTl~ 10shy 0

0 -Q) ~ (0 CA (0

U) CJ) e01 ()en r en

100 --Jt bU --J jl

10-4

120 130

Fig 9

140 150 160 110 180 190 200

Neutron Energy (MeV)

(n2n) cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 41: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

ZINa (n 7 ) 10-3

co c L c

c

c 0

0 CD

en ~

co co 0 L

cgt

10-4

I

- -shy shy

J

-

~ -c tIl

a tIl

0

10 -J

b -J +gt

IV __ _51 I

Fig 10 (ny) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 42: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

NA-23( N P)

Trd

en C Lshya

c 10-2

c 0

EVALUATED MAT NO BMITRAt 66 ---I U EVALUATED-DELTA MAT NO S RBASSt 66 Q) EVALUATEOtDEl TA MAT NO RPRASAOt 66

tf) w 0 E B PAULt 53 bull JCSIKAlt 67 l A CSKHURANAt 60 0 F FlESCHt 67en

en e MBORMANNt 60 0 APASQUARELlI 6110-30 SKMUKHERJEEt 61 W SCHANTl 70 L-

8amp CFWILlIAMSON 61 (f) CMBARTlE 75U

Dl ALLAN 61 CMBAIULE 75

0 Dl AllAN 61 CMBARTLE 75 [J JPICARDt 65 reg HWEIGMANNt 82

JE STRAINt a J JANCZYSlYN 82bull65 ~ CSKHURANAt 65 0gt RPEPElINKt 0 RBASS+ 0 RBASSt

10-41

gttTl ~ ~ G rn G ~

t=lr

0 -J

b -J jo

50 100 150 200

Neutron Energy ( MeV)

Fig 11 (np) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 43: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

NA-23(N A )

I 10-1

F

I 10-2

E

10-3

- I -9shy -9shy

I bull I -~~~ttl gt----laquorshy-~ _bullbullbull-----__ ~ T 9

~ JIIIftlmhlt ~ ~ I 111111 PII III

shy_ashy

1

i +

lIAT NO lIE f FLESCHt 67

en c Lshya

c

c 0

0 Q)

I en ~ en

tJ)

0 Lshy

U

10-4

50

Fig 12

1 I

100

EVALUATED DVALUATED-DELTA DVALUA TEDtDELT A

0 lIBORlIANNt A CfWILLIAlISON 0 SKlIUKHERJEEt + PG B I ZZETI t

JCSIKAltbull ltgt JPICARDt bull JESTRAINt 0 GWOELfERt i1 RBASSt 0 GWOELFERt

RBASStbull

150

) shytI1 ~-~ (p Ugt (p

a r

0 -l

6 -l ~

lIAT NO MAT NO

60 61 61 62 63 65 65 66 66 66 66

0 J JANCZYSZYNt LSANCHEZtbull

~ C BARTLE 0 APDEGTJAREVt bull PNNGOCt 0 HWEIGWANNt 0 R PEPELlNKt

DALEICHtbull

73 7 4 75 77 80 82 85 85

200

Neutron Energy (MeV)

(na) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 44: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

Z~Na (n n A) 0401r-----r-----T-----~----~----_----~----~----~----~~--_

JENDL-32

U) reg 66 WOELFER+

C Lshy0

0

C 0

020

~ ~ ~0

CD

(I

tA) en ~

10 ~ r

I U) I

U) I 0 I -J0 I bLshy I -J

c) __ J ~010

O 001 k ~ (-) il - - 100 150 200

Neutron Energy (MeV)

Fig 13 (nna) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its

standard deviations

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 45: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

Z5N a (n n P) 040-----~~----~----_------~----_~r-~~-----T------r------r----_

(I)

c Lshya

-c

c 0

030

020

o JENDL-32

85 LEICH+

I

I J

J

I I

J

I I

I

I I

I

I I

I

I

I I

I I

I

I

I I

I

I I

I I

f

150

200

~ -0 ~ (lj til (lj

Q)

en 0 ~

T(I)I (I) 0

-)0 6Lshy-)

() j

Neutron Energy (MeV)

Fig 14 (nnp) reaction cross section of 23Na The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 46: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97 -07 4

Na-23

30

- ~ - ~ ~ 20(l)

0 U ~

~ ~ 0 ~ 100 t=

WJ

Neuron Energy (Me V)

Fig 15 Error of the 1 st order Legendre-polynomial coefficient for 23Na

- 41shy

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 47: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

-shy -shy

3

lAERI-Research 97-074

Total Cross Section of Fe

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 7 4 Schwartz+

i

2 Neutron Energy (MeV)

Total cross section of natural iron below 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 42shy

1

c o +- (J CD

Cf)

en en o () ~

8

6

4

2

o

Fig 16

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 48: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97-074

Total Cross Section of Fe

0

C 0 +-U Q)

Cf)

en en 0 ~

() 2

-GMA fit o 70 Carlson+ o 68 Cierjacks+ o 72 Perey+ A 73 Pattenden+ v 74 Schwartz+

4 8 12 16 20 Neutron Energy (MeV)

Fig 17 Total cross section of natural iron above 3 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 43shy

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 49: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

- JJ - Q 0

bull -4~ u (l)

CZl 01 rJj rJjI 0t U ~

02~~~~~--~~--~~--~~--~~--~~--~~--~

GMAfit ltgt 58 Terrell+ 0 62 Bormann+ 0 64 Santry+ b 66 Liskien+ + 75 Smith+

x o v

78 Ryves+ 88Ikeda+ 89 Li Chi-Chou+

II I I

IIlt

G1 ~ ~ (l) ~ r

C J

b J Jgt

001 5 10 15 20

Neutron Energy (MeV) Fig 18 (np) reaction cross section of 56Fe

The solid line stands for the best estimate and the dashed ones standard deviations

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 50: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

Fe (nYl

~

CJ)

----------~------ --ampshyc 10-3 shy -- - ---~ ~ ----------shya c -

I Ic I I

I I I I-0 10-4 I

I ~ I-+-I ~JENDL-32 VlU (lI~

U1 Q) ~ o BCDIVEN+ 60 r Ien

0AVMALYSHEV+ 64 reg I -l

CJ) 10-5 A MBUDNAR+ 79 I b -l

j

0 I I I

CJ)

shyI I I

I u I I I I I I I I

10 -81 I I I I I10 6 2 3 4 5 6 7 8 g1n7 2

Neutron Energy ( eV) Fig 19 (ny) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 51: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

080

---------shy

JENDL-32 -f tI1

0-0 VJASHBY+ 58 (II rn (II

0 VJASHBY+ 58 e () r

A OASALNIKOV+ 72 0 J

~ GFAUCHAMPAUGH+ 77 b J ~88 JFREHAUT+ 80

Fe (n2n)

070 (J)

C L 060C

c - 050 c a shy 040 -I- U Q)~

I en 030

(J)

(J) 020 a L

u O 1 0

OOO~I----~----~----~----~----~--~----~----~----~----~ 100 150 200

Neutron Energy (MeV) Fig 20 (n2n) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 52: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

--

Fe (na)

en 010 c JENDL-32 f shy0 A HHAENNI+ 52c

reg VVVERBINSKI+ 57008- o FLHASSLER+ 62

c 0 shy

(II

~006 -I-J -~

00U ~ CD ~

rCI) - gtC004 -J

ben --J faoen 0

- ooz u

1 _ bull steftO 00

O0 100 200

Neutron Energy (MeV) Fig 21 (na) reaction cross section of natural iron

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 53: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

Fe 30~----~----~----~----~~

~

~ -

~ (J) 0 U -1

~ t+-I 0

0 ~

t= ~

20

10

Neuron Energy (Me V)

Fig 22 Error of the 1 st order Legendre-polynomial coefficient for natural iron

-48shy

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 54: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

61 ~

51 ~

4 r e )- 3cO 0

I 100shy

JJ2

0

U-235(nf)

6

__~_ _____bull a ___bull __-c___bullbullbull____-bullbull __

1 100

5 ~ 7wl____ 801

4 ~ 6Q gt3 60 tTl

~ I 40 ~

(1)

2 V AO (1)

e~ ()20 r ~ 20

0 -l~

)0shy 0 b )0-

0 -l

f j

20 nfl-I [ ~ ~I_I

~ ~0

6 cq laquolt-0~~

Fig 23 Covariance of the fission cross section of 235U

1 X- 1 1~ 1- 1- J ~ ~ L~

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 55: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

Total Cross Section of 235U

c o +-U (J)

- GMAfit o 66 Uttley+ [J 72 Boeckhoff+ o 73 Green+ v 74 Schwartz + a 81 Poenitz+

~ 10 en o s

U

5~~~~~~----~--~--~~~~~

10-1 10deg Neutron Energy (MeV)

Fig 24 Total cross section of 235U below 1 MeV The solid line stands for the best estimate and the dashed ones standard deviations

- 50shy

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 56: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

JAERI-Research 97 -074

Total Cross Section of 235U 10

GMA fit 0 71 Foster+ 0 73 Green+ v 74 Schwartz + - c 8 a 81 Poenitz+

c 0 83 Poenitz+ 0

u Q)

C)

en en 0 shy()

4~~--~----~--~--~--~~--~--~5 10 15 20 Neutron Energy (MeV)

Fig 25 Total cross section of 235U above 1 Me V The solid line stands for the best estimate and the dashed ones standard deviations

- 51shy

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 57: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

U-23S(N2Nl

(J)

I C I

----- L I

shy

c

C

- ----

c 0

I- I ~I I 0

1-1 ~ I

~U JENDL-32 I I ~

C11 N Q)

o D S MATHER+ 72 ~ en I 0reg JFREHAUT+ 80 I

-J (J) o

I

--------- -J

(J) Jgt

0 ~-------------- -- shy

L U ~

00 I

50 100 150 200

Neutron Energy (MeV) Fig 26 (n2n) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 58: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

U-235(NYl1 0 1

JENDL-32 ~ o JCHOPKINS+ 62

CfJ reg VNKONONOV+ 71 A RGWIN+ 76C

10deg shy cfP RGWIN+ 76o c 88 FCORVI+ 82 - o FCORVI+ 82

c gto 10-1

~ -I-J

~ COU ~

cn Q)w ~ en 0 -J

ben -J -+-CfJ 10-2

o shyu

Neutron Energy ( eV) Fig 27 (ny) reaction cross section of 235U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 59: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

235U NU-P 60 111111111 I 11111111 111111111 111111111 111111111 111111111 111111111 111111111 11111111

JENDL-32

o J FREHAUT + 80 reg JFREHAUT+ 82

o REHOWE 84

c lt-t )shyI tr130 tlJ

z ~ (II

cn jIo ~

rI

0 -l

b -l ~

oO( 111111 IIUII ft 1111 UII I 1111111 1111( (I II1111 I IIl11g 11110 7 I

Neutron Energy ( eV) Fig 28 A verage number of prompt neutrons emitted in fission

The errors are hardly visible since they are less than 1

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 60: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

--------------------------------------------------------------------------------------------------

235U NU-D o 030 I II 11111 I I I 111111 I I 1111111 I I 111111 I I I 111111 I I I 111111 I I I 111111 I I I 111111 I I 111111

0020

-c I ~

~J z

rJO

cn

----- JENDL-32

I I

I~ -

--11-

I 1

74 78 78 79 83

HROSE+ 57 (1)

~ WRSLOAN+ ~ cn bull ~

reg W I MC GARRY + 60 KLKRATZ r

0

A CFMASTERS+ 69 -l0010

El GENGLER+ b reg CFMASTERS+ 69

-l

SSYNETOS+ reg JFCONANT+ 71 ~ PLREEDER+ ~ AEEVANS+ 73 38 AEEVANS+ 73i

~

o 000 d 1111111 I I 11111 bull I II I I 111111 I I 1111 I I I I I I 1111 I I

bull 10-1 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Neutron Energy ( eV) Fig 29 A verage number of delayed neutrons emitted in fission

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 61: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

IAERI-Research 97-074

U-235 10~----~----~----~----~~

8~

~ ~

~ ~ (jJ 60

U ~

~ ~ 4 0

0 ~

~ ~

~ 2

Neuron Energy (MeV)

Fig 30 Error of the 1 st order Legendre-polynomial coefficient for 235U

- 56shy

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 62: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

T atal Cross section of 238U

12

GMA fit 0 58 Bratenahl+ 0 60 Peterson+

cl10 0 71 Whalen+ --

c 0 +-u CD

C) CJ) CJ)

0 ~

0

A 71 Foster+ v 81 Poenitz+ x 84 Tsubone+

8

6

10-1 1 0deg 101

Neutron Energy (MeV)

Fig 31 Total cross section of 238U

The solid line stands for the best estimate and the dashed ones standard deviations

- 57shy

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 63: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

231U (n 2n ) 20rl --~--~--~--~-----~--~--~--~-----~--~--~--~---

JENDL-32(I)

c reg 78 VEESER+ - r reg 79 KARIUS+C

EI 80 FREHAUT+c

c 10 )shy10 trJ tl I-lt

U ~ (1)I CD Zl (1)

amp en ~ r(I)

(I) 0 -l0 I

0 -l

shy ~ Jtcgt c

00 4JI

50 100 150 200

Neutron Energy (MeV)

Fig 32 (n2n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 64: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

---

----

231U (n3 n ) 20~------~------~------~------~------p-----~~----~------~-------r------~

en JENDL-32

t-C

reg 78 VEESER+o 0

C

0

Q)

en

0 I

f~~--~+----~----cn lt0

en

en 0 t-

cgt

00middot -=== 100 200

Fig 33

150

Neutron Energy (MeV)

(n3n) reaction cross section of 238U

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

gt ~-~ VJ (D

~ r

0 -l

b -l jgt

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 65: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

9 8 1

r6R

01 v5 0

I (5 4 ~ 3

iJJ 2 1 0

U-238(nf)

100 9 8 SO 1

606 5 -i

gt1pound 40 lt10 tI14 v ~

3 sect 0 shy(l) 2 lt0 (I) (l)2 ~ e ()0 r

1 0 0 00 -J

c) 20 lt0 b -J jgt

40

gt b- F ~~

lt9 -lt~~0 ltlt--b

Fig 34 Covariance of the fission cross section of 238U

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 66: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

ZSIU (n ( ) 10

JENDL-32

10deg =- 58 PERKIN+ reg 71 FRICKE

71 DRAKE (I) y 72 PANITKIN c 75 POENITZ shy 0 76 DABLETSHIN+0

c A 76 LINDNER1 0 -I ~ I WWOgcamp ~ji ~

~ 80 HUANG+ 82 MCDANIELSc bull

0 ~ ~w reg 86 KAZAKOV+

88 BULEEVA+ 0 CD

U) 10-2 0)

(I)

(I)

0 shy

c)

H~---

10-4 I I I

lOG 10 7

Neut ron Energy ( eV)

Fig 35 (ny) reaction cross section of 238U

gttrl 0-~ CIgt (1)

e ()

r

0 -l

b -l +

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 67: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

U-238

~

~ - 2 ~ (l) 0

U ~

~ ~ 0 1~

~

Neuron Energy (Me V)

Fig 36 Error of the 1 st order Legendre-polynomial coefficient for 238U

- 62shy

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 68: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

Total Cross Section of 239pU

c o

u

o

CJ

ltgt A

GMA fit 71 Foster+ 73 Nadolny+ 74 Schwartz+ 83 Poenitz+

Q) 6 (f) (J) (J)

o ~

()

4~~----~--~----~----~--~----~ 8 12 16 20

Neutron Energy (MeV)

Fig 37 Total cross section of 239PU

The solid line stands for the best estimate and the dashed ones standard deviations

- 63shy

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 69: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

--

Zllp U (n 2n ) 0801~------------~--------+---~--~~------~----~--~------------~--~

070

JENDL-32

~t~l f I I

reg [E]

72 MATHER+ 85 FREHAUT+CD

c a L- O50~a

c 0

-

) ~

0 ~ I CD en

til (ll

~ ~-_ rCD - ----shyI CD

0 -J0

L- b -Jc) n n ~

0001 Imiddot

50 100 150 200

Neutron Energy (MeV)

Fig 38 (n2n) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 70: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

Z31P u (n r ) 10 1

10deg F JENDL-32

0 56 SPIVAK+ reg 62 HOPKINS+

en 0 71 KONONOV+ C ~--~~ x 0 shyc

c 10-1

~-J~_ c 0 I- -I gt

tTl tI I -0 tI

(Tgt CZgt (Tgt

OJ (J) en 10-2 CJ1 ~ ren

en 0 -l 0 b shy -l cgt ~

10-3

1 0 - 4 I I I 1 I eftS lOG 10 7

Neutron Energy ( eV)

Fig 39 (ny) reaction cross section of 239PU

The solid line stands for the JENDL-32 curve and the dashed ones its standard deviations

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 71: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

Pu-239(nf)

100 100

7 8080

67 605 r6 60 -4

gt ~S 4 trJ40 tl 4 3 c

40 ~

I - 0 CIl (1)202~ 3 ~ 20~ - ~ llJ 2I loshy o 0

0 -J

1 0 b -J---

loshy

-200 ~

~s- -20 ~ -40

~lt ltgt _- ~

ltgt lt

lt5_ ~iii-- ~

ltrlt--lt q~~ cgtbull G2

cgt iC9sshybull Cgtgts-

Fig 40 Covariance of the fission cross section of 239pU

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 72: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

14

Optical model calc 12 A 74 Schwartz+

- 0 81 Poenitz+ Jj

0 83 Poenitz+ -

= 100 ~ ~

u (l)

CZl 8rJJ rJJ 0 1-4 U 6

Neutron Energy (e V)

Fig 41 Total cross section of 239Pu obtained with the optical-model calculations The lower figure stands for the uncertainties in the calculations

- 67shy

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy

Page 73: DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~ 97-074 . dec 1 9 . 1997.~ estimation of covariances of . 16. 0, 23na, fe, 235u, 238u

lAERI-Research 97-074

Pu-239 10~----~----~----~~

8~

~ - ~ ~

Cl) 60

U ~

~ ~ 4 0

0 ~

t ~ 2

Neuron Energy (Me V)

Fig 42 Error of the 1st order Legendre-polynomial coefficient for 239Pu

-68shy