MEASUREM

TO FISSIONS

OF

NYO - 10210MITNE- 36

ENT OF THE RATIO OF FISSIONS IN UIN U2 3 5 USING 1.60 MEV GAMMA

THE FISSION PRODUCT La 14 0

byJ. R. WolbergT.J. ThompsonI. Kaplan

August 19, 1963

Contract AT (30-1) 2344U.S. Atomic Energy Commission

Department of Nuclear EngineeringMassachusetts Institute of Technology

Cambridge, Massachusetts

238

RAYS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

DEPARTMENT OF NUCLEAR ENGINEERING

Cambridge 39, Massachusetts

MEASUREMENT OF THE RATIO OF FISSIONS IN U 238

TO FISSIONS IN U235 USING 1. 60 MEV GAMMA RAYS

OF THE FISSION PRODUCT La 1 4 0

by

John R. Wolberg, Theos J. Thompson, and Irving Kaplan

August 19, 1963

MITNE - 36

NYO-10210

AEC Research and Development Report

UC-34 Physics

(TID-4500, 18th Edition)

Contract AT(30-1)2344

U. S. Atomic Energy Commission

TABLE OF CONTENTS

INTRODUCTION

DESCRIPTION OF THE METHOD

USE OF THE METHOD FOR CALIBRATION OFINTEGRAL COUNTING EXPERIMENTS

BIBLIOGRAPHY

1

2

9

14

ABSTRACT

This paper describes a method for measuring 628, the ratio of fissions238 235in U to fissions in U The method was developed as a part of the

D 2 0 lattice program at M. I. T.; however, it can be used for measurements

in any thermal reactor of natural or slightly enriched uranium.

The fast fission factor in uranium cannot be measured directly. It is,

however, related to 628 which can be measured:

1 + C 6 28,

238 235where C is a constant involving nuclear properties of U and U2. All

previous methods of measuring 628 utilize a comparison of fission product28 235

gamma or beta activity in foils of differing U concentration irradiated

within a fuel rod in the lattice. A double fission chamber is then used to

relate the U238 and U 2 3 5 fission product activity to the ratio of the

corresponding fission rates. Most of the experimental uncertainty associated

with the measurement of 628 is generally attributed to the fission chamber

calibration.

The method developed at M. I. T. avoids the need for a fission chamber

calibration and is accomplished directly with foils irradiated within a fuel

rod in the lattice. Two foils of differing U235 concentration are irradiated

and allowed to cool for at least a week. The relative activity of the 1. 60

Mev gamma ray of the fission product Lal40 is determined for the two foils.

This ratio , the foil weights and atomic densities, and the ratio of fission

yields 2 for La140 are then used to determine 628. This value of 628

is used to calibrate simpler measurements in which the relative gamma

activity above 0. 72 Mev is determined for sets of foils irradiated in fuel

rods of the lattices of interest. The energy 0. 72 Mev is a convenient dis-

crimination level, as it is the maximum energy of bremsstrahlung from2392. 3 d Np 2 .

This method appears to offer the advantages of direct measurement and

increased accuracy (the major uncertainty being the ratio ofsP2 5 / 28 of La 40

In addition, the results can be improved as better fission product yield ratio

data become available, and the method facilitates comparison of 628 values

obtained by different laboratories.

1

MEASUREMENT OF THE RATIO OF FISSIONS IN U238

TO FISSIONS IN U 2 3 5 USING 1.60 MEV GAMMA RAYS

OF THE FISSION PRODUCT La14 0

John R. Wolberg,* Theos J. Thompson, and Irving Kaplan

Massachusetts Institute of TechnologyCambridge, Massachusetts

United States of America

Introduction

This paper describes a method for measuriig 628, the ratio of fis-238 235

sions in U to fissions in U 3 . The method was developed as part of the

D20 lattice program at M. I. T.; however, it can be used for measurements

in any thermal reactor of natural or slightly enriched uranium.

The fast fission factor in uranium cannot be measured directly. It is,

however, related to 628 which can be measured:

E = 1 + C 628'

238 235where C is a constant involving nuclear properties of U and U2. All

previous methods of measuring 628 utilize a comparison of fission product235-

gamma or beta activity in foils of differing U concentration irradiated

within a fuel rod in the lattice. A double fission chamber is then used to

relate the U238 and U235 fission product activity to the ratio of the corre-

sponding fission rates [1, 2]. Most of the experimental uncertainty associ-

ated with the measurement of 628 is generally attributed to the fission

chamber calibration.

The method developed at M. I. T. [3, 4, 5] avoids the need for the fission

Now at Technion, Israel Institute of Technology, Dept. of Nuclear Science,Haifa, Israel.

2

chamber measurement and is accomplished directly with foils irradiated

within a fuel rod in the lattice. Use of the method for calibrating simpler

integral counting measurements is possible, and this procedure has been

adopted at M. 1. T. The method appears to offer the advantages of direct

measurement and increased accuracy (the major uncertainty in the meas-

urement being the ratio of p2 5 to P28 of La 4 0 , where the s's are the fission

product yields). The results can be improved as better data on the fission

product yield ratio of La 4 0 become available, and in addition, the method

facilitates comparison of 628 values obtained by different laboratories.

Description of the Method

Previous research by the authors [3, 4] has shown that the only impor-

tant fission product gamma ray with an energy above 1. 2 or 1. 3 Mev in the

time interval from a week to several months after irradiation of a uranium

foil is the 1.60 Mev gamma ray of Lal 4 0 . This nuclide has a 40h half-life,

but reaches equilibrium with its parent, 12. 8d Ba' 4 0 . The mass 140 chain

has a high fission product yield, and 88 per cent of the La 4 0 disintegrations

result in the emission of a 1.60 Mev gamma ray. The method under consid-

eration utilizes the ratio of the count rates of foils of differing U235 concen-

tration at a channel centered at 1. 60 Mev in a gamma ray scintillation

spectrometer. This ratio can be related to 628 without the need for an addi-

tional calibration experiment.

To derive the relationship in its most general form, three subscripts

denoting the isotopic concentrations of the uranium are introduced. The

subscript 1 corresponds to the isotopic concentrations of the depleted foils;

2, to those of the second foil; and 3, to those of the fuel. The measurement

requires two foils of differing composition. The U 2 3 5 concentration is as

small as possible in the .depleted foil. The U235 concentration of the second

foil may equal the U235 concentration of the fuel, or it may be some other

known enrichment. The usual enrichment in this case is the natural isotopic

mixture present in naturally occurring uranium; often foils of the same

enrichment as the fuel are not available. In the M. I. T. measurements, the

second foil was always of natural uranium. We shall define y as the ratio

of the number of counts from a depleted foil and a second foil of differing

3

enrichment which have been irradiated simultaneously. The foils are counted

at a channel centered at 1.60 Mev with a gamma ray scintillation spectrom-

eter. The measured count rates should, of course, be corrected for back-

gro'und, dead time, and differences in foil weights. It has been shown [3, 4]

that if the measurements are made in the time interval from a week to sev-

eral months after the irradiation, the counts in this channel result primarily

from 1.60 Mev gamma rays of the fission product La40 For each foil the

count rates are the sum of counts originating from La14 0 nuclides born by235 Z38

fission of U and by fission of U2. Hence,

f~) 28 00c 28 ~ 25 00 0-2 d

f(t) P2 8N2 * (E) of (E) dE + f(t) P25JN 1 *(E) f25E) dET 0

I-= T . (1)

f(t) pN 28 O(E) o28(E) dE + f(t) 2 5N25 co *(E) -25(E) dE

In this equation f(t) is the number of counts measured per unit time per Lal 4 0

nuclide as a function of time. An explicit expression for f(t) could be written,

but an examination of equation (1) shows this to be unnecessary as f(t) cancels

out of the equation. The neutron flux in the energy interval dE at energy E,

averaged radially over the rod, is denoted by 4(E) dE. The formulation of

the problem is not affected by neglecting the spacial variation of the flux.238 235

The N' s are the atom densities of U , (28), and U , (25), in the two140 238 235

foils; the P ' s are the fission product yields of La from U and U

fission; and E T is the U 2 3 8 fission threshold energy. The lower limit of the

integral containing ET could have been written as 0, because the fission

process in U 238 is a threshold reaction. That is,

ET 28 (E) (E) dE = G28(E) (E) dE, (2)

since

a28(E) = 0 for E < 0 < E. (3)

238 235The quantity 628 is the ratio of fissions in U to fissions in U in the fuel,

and can be written:

4

N28 00 28(E) $(E) dE

628 "= ET (4)

N 25 0 25 (E) $(E) dE

Using the following definition:

0 a 28(E ) $(E ) dE128 T ()

25 025(E) $(E) dE'0

and dividing the numerator and denominator of Eq. (1) by N 25'I~2 N2 25'

28 1 28 + N1

N25 N 2 5

=-2 5N 2 125 2(6S28(6)

2 8N 2 8 + 1PN251

2 5N 2 25

From equations (4) and (5), it follows that

2528 N 3

125 N 2 8 628. (7)3

Substitution of Eq. (7) in (6) yields

28 25 N 2 5

132 8 N NN 3 N125N28 628+ N2 8

1y2 N=N 2(8)28N 2 8N 2 5

25N25N28 6 + 1PN25 N28 628+

12 5 2 N3

Equation (8) can be rearranged to solve for 628:

5

p 2 5

628

^y -

(9)28N 2

N1 28N1

Expressions for the quantities N28 N28 and N28/N28 can be obtained. If it3 1 as 2sue ta 1

is assumed that

N25 + N28 = 25 + N281 N 2 + 2

N12 (R1 + 1) N N2 8 (R2-+-1)

= 25 + N 28= 3 N3 ,

N N 2 8 (R + 1),

R. = N2/N21 1 1

From Eq. (11) we get

N28 1+ R N 2 8 1+ RN3 =1+R1 2 -a.

N28 1 + R 3 a 3 N 2 8 1 + R 21 1

Substitution of Eq. (13) into (9) gives

628

N 25$25 N 2 I

N2 5 a 3 ~P28 N 3 j

1 - a2y

p25 F,28_

(10)

(11)

(12)

(13)

(14)

S = R /R 3, (15)

and F is the ratio of counts that would originate from U 2 3 8 fissions to counts

that would originate from U 235 fissions in a foil of the same composition as

the fuel. When the U 2 3 5 concentration of foil 2 is the same as the U 2 3 5 con-

centration of the fuel, a3 = a2 = a, and equation (14) reduces to the form

then

where

where

&

pav - S62 2 5 aY-S(16)

28 2 8 1 - avY

Equations (14) or (16) are used to determine 628 after the ratio y has been

calculated from the count rates of the two foils. The procedure for deter-

mining 628 follows-.

1) A counting system similar to the one shown in Fig. 1 is calibrated for

the 1.60 Mev gamma ray. This peak can be found directly by using the

La 1 4 0 peak from irradiated uranium foils. The channel width should be

set to satisfy three conditions:

(a) high ratio of counts to backround,

(b) low sensitivity to drift,

(c) large count rate.

Condition (a) is improved by decreasing the channel width and (b) and

(c) are improved by increasing the width, so that the chosen width

should be a compromise among the three conditions. A width of 5. 5

volts was used in the M. I. T. experiments and the calibrated base line

setting varied from 53 to 54 volts. The width was, therefore, about

10 per cent of the base line value, and corresponds to about 0. 16 Mev.

All gamma rays with energies between about 1. 52 Mev and 1. 68 Mev

were, therefore, counted.

2) The foil backrounds are determined. Using a 1-3/4-inch X 2-inch

NaI(Tl) crystal and 1-inch diameter foils, the backrounds were about

11 counts a minute. About 6 of these 11 counts per minute were from

general backround, not originating from the foil.

3) The foils are positioned within a full rod in a manner similar to that

shown in Fig. 2, and are then irradiated at the desired position within

the lattice. The lattice facility is described in an accompanying paper.

In the M. I. T. experiments, several sets of foils were irradiated simul-

taneously and the irradiation times were approximately one day.

4) The rods containing foils are removed from the lattice after a suitable

"cooling off" period, and the foils are removed from the rods. The

foils are then allowed to cool for an additional period until the activity

BAIRD ATOMIC4815 BLS CINTILLATIONPROS E-

EQUIPMENTLA' 40 ACTIV

USEDITY

TO MEASUREOF THE FOILS

FIG. 1

SLIGHTLYENRICHEDNATURALURANIUMFUEL

FIG. 2 FOIL528

0.002" Al0.005" NAT.0.002" Al0.005" DEP.0.002"AI

ARRANGEMENTMEASUREMENTS

U

U

FOR

9

within the channel at 1.60 Mev is predominantly from L40. This

condition is fulfilled about a week after the irradiation.

5) The 1. 60 Mev activity of each foil is counted. The counting can be

repeated daily for several weeks to improve the precision of the meas-

urement. The system must be calibrated daily and the backround must

be checked periodically. In the M. I. T. experiments the depleted

uranium foils contained 17. 7 p. p.m. U 2 3 5 and the initial count rates

were about 10 times backround. The second foils were of natural

uranium and the initial count rates were about 200 times backround.

The corrected count rates decreased with the expected 12. 8 day half

life.

6) The values of y are determined and values of 628 are calculated from

equations (14) or (16). The values of y for each set of foils should be

constant within statistical limits for several months after irradiation.

In the M. I. T. experiments, the measured values of y and the calcu-

lated values of 628 were constant within the expected limits.

Use of the Method for Calibration of Integral Counting Experiments

The main advantages of the La140 technique have already been mentioned.

These include improved accuracy and the elimination of the need for a cali-

bration experiment which utilizes a fission counter. The main disadvantage

of the method as compared to the integral gamma counting technique devel-

oped at WAPD [1] or the beta counting technique developed at BNL [2] is the

need for long irradiation and cooling times. In addition, the foils cannot be

reused for the duration of the counting period which can last up to several

months after the irradiation. By using the La410 technique as a calibration

measurement for integral counting experiments, the advantages of both

methods can be realized. This procedure was adopted at M. I. T.

For either the gamma of beta counting technique, equations similar

to (14) and (16) can be derived. These are:

10

N25

P(t) 25 aMt - S

N36 28 = P(t) F(t), (17)

28 1 - a2 y(t)

which becomes

P(t)[ay(t) - S]628 = = P(t) F(t) (18)

28 1 - ay(t)

25when N 2 equals N3 . In these equations y(t) is the ratio at a time t after

the irradiation, of the measured fission product activity in the depleted ura-

nium foil to the activity of the second foil. The activities should be corrected

for backround, dead time, and differences in foil weights. The function P(t)

is the number of counts measured per U238 fission per unit time as a function

of time after irradiation divided by the number of counts measured per U 2 3 5

fission per unit time as a function of time after irradiation. The function

F(t) is the calculated ratio, at time t, after irradiation, of counts that would

originate from U238 fission products to counts that would originate from

U235 fission products in a foil of the same composition as the fuel. The

functions y(t) and P(t) are dependent upon many variables including the

experimental method, the irradiation time, and the exact experimental set-

up; however, if determined correctly, the calculated value of 628 should

be independent of the time after irradiation at which the ratio y(t) is deter-

mined. The calculated value of 628 should also be, of course, independent

of the experimental method, irradiation time and the experimental setup.

The M. I. T. measurements utilized the Westinghouse integral gamma

counting technique to determine functions y(t) and the La14 0 method to deter-

mine the function P(t). A gamma-counting rather than a beta-counting tech-

nique was chosen for several reasons.

1) Beta-counting methods are more sensitive to handling procedures

because they require catcher foils. As many as 12 Al catcher foils

are used in the measurement of 628 and these thin foils must be

carefully positioned to get consistent results. Special care must be

taken not to wrinkle the foils when they are inserted into the fuel rod.

11

2) The results of experiments using beta-counting techniques are sensi-

tive to the condition of the surface of the uranium foils, while 'gamma

counting results are not. Movement of fission products from the ura-

nium foils to the catcher foils is affected by the oxide on the uranium

foil surfaces, so that care must be taken to remove all oxide from the

foil surfaces if beta-counting is used.

3) Gamma-counting methods are less sensitive to foil thickness. The

energies of the gammas counted in all gamma-counting methods are

great enough so that self-shielding is negligible in uranium foils sev-

eral mils thick. Beta-counting methods could be devised which do not

require the use of catcher foils but self-shielding would still present

a problem, and the results might depend on foil thickness.

The procedure adopted at M.I. T. follows.

1) A value of 628 is determined at a known position in a test lattice using

the La140 technique.

2) Additional foils are irradiated at the same position for a shorter period

of time. These foils are then used to determine the ratio y(t) with an

integral gamma counting setup similar to the one shown in Fig. 3. For

lattices of 1-inch rods the irradiation time was standardized at 4 hours.

Four hours was also a convenient irradiation time for resonance cap-

ture and thermal utilization measurements which were often made

simultaneously with the fast fission measurements.

3) Using equations (17) or (18), the function P(t) is determined. This is

a unique function for the given experimental conditions and must be

redetermined only if the conditions are changed.

4) Values of 628 for subsequent lattices are measured by determining

values of y(t) from foils irradiated in the lattices and combining these

values with the corresponding values of P(t) according to equations (17)

or (18). A data reduction code written for the IBM-7090 digital com-

puter is used to analyze the M.I. T. data.

BAIRD ATOMIC#815 BLSCINTILLATIONPROBE

FOIL

FIG. 3

BETA

S HIE LD

EQUIPMENT FOR MEASURINGACTIVITY OF THE FOILS

GAMMA

13

The integral gamma counting technique used at M. I. T. differs fromthe Westinghouse technique (1) in one significant manner; a bias setting of

0. 72 Mev has been chosen rather than the Westinghouse setting of 1. 20 Mev.

Since the purpose of the experiment is to determine the ratio of fission prod-

uct activity in the two foils, the number of counts coming from U238 capture

reactions and subsequent beta decay must be small. Consider the capture

reaction and the decay chain of the resulting U239 nuclide:

138 239 23m 292. 3 d 239U + n - U > N 2 3 9 + P(1. 2 Mev) 23 + P23 + p(0.72 Mev)p u

(19)

The gammas associated with these beta decays have lower energies than themaximum beta energies; but even though a beta shield is used, there is

bremsstrahlung with a maximum energy equal to the maximum energy of the

betas. If counting starts before most of the U239 is allowed to decay, a sig-

nificant fraction of the counts of the depleted foils may come from brems-

strahlung with energy above 0. 72 Mev and originating from the U239 betas-.

The 0. 72 Mev bias setting insures that no bremsstrahlung originating from

the 39 betas will be counted. A cooling period of three hours is long enoughp 239to insure a negligible contribution from the U beta activity.

The Westinghouse technique requires a bias setting of 1. 20 Mev which

makes the three-hour cooling period unnecessary. As soon as the foils canbe removed from the rod, the counting can begin. The advantage of using a

setting of 0. 72 Mev and waiting three hours is that the ratio of dose rate to

the experimenter to count rate is reduced by a factor of about ten. Byreducing the bias setting from 1. 20 to 0. 72 Mev, the count rate is increased

by an amount which just about compensates for the loss of fission productactivity in the three-hour cooling period. But the radiation level associated

with the rods three hours after irradiation is only about one-tenth the levelat a half-hour after irradiation.

Another advantage of using a 0. 72 Mev bias setting rather than a 1. 20Mev setting is that the foils are counted at a longer time after irradiation

with the result that the change in count rate per unit time is smaller. There

is, therefore, a smaller uncertainty in count rates owing to uncertainties

in time.

14

Bibliography

[1] Kranz, A. Z. WAPD-134 (1955).

[2] Kouts, H., G. Price, K. Downes, R. Sher, and V. Walsh, PICG 5,183 (1955).

[3] "Heavy Water Lattice Research Project Annual Report," Chapter 5,NYO-9658 (September 30, 1961).

[4] Wolberg, J. R., T. J. Thompson, I. Kaplan, "A Study of the FastFission Effect in Lattice of Uranium Rods in Heavy Water," NYO-9661(Feb. 21, 1962).

[5] Weitzberg, A., J. R. Wolberg, T. J. Thompson, A. E. Profio, I. Kaplan,"Measurements of U 2 3 8 Capture and Fast Fission in Natural Uranium,Heavy Water Lattices," Trans. ANS, 13-5, Vol. 5, #1 (1962).