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Transcript of DEC 1 9 1997.~ - Fermilablss.fnal.gov/archive/other/jaeri-research-97-074.pdf · jaeri-research ~...
~ 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
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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
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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)
- 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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- 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
copy
v~ ~ Ii B~yh~Jf~J-1fr6~=1iEMI~fljGlPG~Jf~yenfH~f-rTo
A-yenO)rciJ1fb1tli B~fh~Jf~J-1fr~~Jtil~$~Jf~m~~ (=r319-11 ~~~jj~JiiJmr
~1) ~l to$G~Gltt~Po 7dto 0)~6)IMDJj~A~-=fh5amp~~Jifl1rshy
(=r 319-11 ~~~jj~JI1JW~1 B~yb~~J-1frlJ) -r1~ J G~1JIiffia- to 7d gt l f5tJTo
This report is issued irregularly
Inquiries about availability of the reports should be addressed to Research Information
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
- 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)
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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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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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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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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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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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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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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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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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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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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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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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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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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
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
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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
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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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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)
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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))
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
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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
- 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
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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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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
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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
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
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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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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
- 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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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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Kiev Vol 2 p119 (1977)
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1971 Vol 1 p252 (1971)
175) Drake D et al Phys Lett B16 557 (1971)
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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)
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
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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
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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
- 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
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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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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
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--
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
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
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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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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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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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86) Glazkov NP et al Atomnaya Energiya lS 416(1963)
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173) Vorotnikov PE et al Proc Int Conf Fourth All Union Conf Neutom Physics
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1971 Vol 1 p252 (1971)
175) Drake D et al Phys Lett B16 557 (1971)
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177) Poenitz WP Nucl Sci Eng 5]300 (1975)
178) Diven BC et al Phys Rev12Q 556 (1960)
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180) Barry JF et al J Nucl Energ 18 481 (1964)
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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)
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
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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
- 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
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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)
- 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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- 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
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
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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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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
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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
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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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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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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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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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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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86) Glazkov NP et al Atomnaya Energiya lS 416(1963)
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112) Allen BJ et al Nucl Phys A269 408 (1976)
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116) Frehaut J et al Private Communication (1980)
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Trans Am Nucl Soc 13 449 (1995)
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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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142) Howe RE Nucl Sci Eng 86 157 (1984)
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147) Clifford DA PhD Thesis Imperial College London (1972)
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19881-282 (1988)
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169) Guenther P et al ANllNDM-16 (1975)
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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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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)
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180) Barry JF et al J Nucl Energ 18 481 (1964)
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183) Huang Z et al LBL-11118 p 243 (1980)
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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)
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
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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
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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)
- 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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- 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
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
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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
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
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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 -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
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
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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)
- 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
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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
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JAERI-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
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
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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
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--
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
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
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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
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
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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
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
References
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Procedures BNL-NCS-51363 p249 (1981)
3) Kawano T and Shibata K Covariance Evaluation System JAERI-DataCode
97-037 (1997) [in Japanese]
4) Igarasi S JAERI-1224 (1972)
5) Igarasi S and Fukahori T JAERI-1321 (1991)
6) Yamamuro N A Nuclear Cross Section Calculation System with Simplified
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7) Raynal J Optical Model and Coupled-Channel Calculation in Nuclear Physics
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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)
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1971 Vol 1 p252 (1971)
175) Drake D et al Phys Lett B16 557 (1971)
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177) Poenitz WP Nucl Sci Eng 5]300 (1975)
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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)
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
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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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)
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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))
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
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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- 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
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
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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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
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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- 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
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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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
JAERI-Research 97-074
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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
JAERI-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
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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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)
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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))
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
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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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
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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
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))
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)
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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
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
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
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
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
--
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
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
- - - - 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
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
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
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
__ _ --~~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
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
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
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
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
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
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
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
-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
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
- 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
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
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
--
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
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
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
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
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
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
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
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
--------------------------------------------------------------------------------------------------
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
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
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
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
---
----
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
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
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
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
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
--
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
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
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
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
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