NYO - 10210
MITNE-
MEASUREM ENT OF THE RATIO OF FISSIONS IN U238
TO FISSIONS IN U 2 3 5 USING 1.60 MEV GAMMA RAYS
OF THE FISSION PRODUCT La 14 0
by
J. R. Wolberg
T.J. Thompson
I. Kaplan
August
19,
1963
Contract AT (30-1) 2344
U.S. Atomic Energy Commission
Department of Nuclear Engineering
Massachusetts Institute of Technology
Cambridge, Massachusetts
36
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 La1 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
1
DESCRIPTION OF THE METHOD
2
USE OF THE METHOD FOR CALIBRATION OF
INTEGRAL COUNTING EXPERIMENTS
9
BIBLIOGRAPHY
14
ABSTRACT
This paper describes a method for measuring 628, the ratio of fissions
238
235
in 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.
however,
It is,
related to 628 which can be measured:
1 + C 6 28,
235
where C is a constant involving nuclear properties of U 238 and U2.
All
previous methods of measuring 628 utilize a comparison of fission product
28
gamma or beta activity in foils of differing U
within a fuel rod in the lattice.
relate the U238 and U
2 35
235
concentration irradiated
A double fission chamber is then used to
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.
crimination level,
2239
2. 3 d Np
The energy 0. 72 Mev is a convenient dis-
as it is the maximum energy of bremsstrahlung from
.
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 Technology
Cambridge, Massachusetts
United States of America
Introduction
This paper describes a method for measuriig 628, the ratio of fis238
235
to fissions in U 3 . The method was developed as part of the
sions in U
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'
where C is a constant involving nuclear properties of U
238
235
and U2.
All
previous methods of measuring 628 utilize a comparison of fission product
gamma or beta activity in foils of differing U
within a fuel rod in the lattice.
235-
concentration irradiated
A double fission chamber is then used to
relate the U238 and U235 fission product activity to the ratio of the corresponding 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 measurement 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 important 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 consideration utilizes the ratio of the count rates of foils of differing U235 concentration 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 additional 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 spectrometer. The measured count rates should, of course, be corrected for backgro'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 several months after the irradiation, the counts in this channel result primarily
For each foil the
from 1.60 Mev gamma rays of the fission product La40
count rates are the sum of counts originating from La1 4 0 nuclides born by
Z38
235
Hence,
and by fission of U2.
fission of U
f~)
28
f(t) P2 8N2
5
~
28
00c
2
1
P25JN
f(t)
+
(E) of (E) dE
*
T
f(t)
pN
d
0-2
f25E) dE
co *(E)
-25(E) dE
0
I-=
T
28
*(E)
00
O(E)
o28(E) dE + f(t)
2 5 N2
5
.
(1)
40
In this equation f(t) is the number of counts measured per unit time per Lal
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.
235 , (25), in the two
238
, (28), and U
The N' s are the atom densities of U
140 from U 238 and U 235
foils; the P ' s are the fission product yields of La
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)
(2)
(E) dE,
since
a28(E) = 0
(3)
for E < 0 < E.
235
238
The quantity 628 is the ratio of fissions in U
and can be written:
to fissions in U
in the fuel,
4
N28
628 "=
N 25
00
28(E) $(E) dE
(4)
ET
0
25 (E) $(E) dE
Using the following definition:
0 a28(E ) $(E ) dE
128
T
25
()
025(E) $(E) dE
'0
and dividing the numerator and denominator of Eq. (1) by
I~225'
N2
N 25'
28 1
28 + N1
N 25
N25
=- 2 5 N 2 125
2(6
S28(6)
8 + 1
2 8N 2
PN251
2 5 N 2 25
From equations (4) and (5),
28
125
it follows that
25
N3
N 2 8 628.
3
Substitution of Eq. (7) in (6) yields
28 25
N2 5
132 8 N NN 3
N1
25N28 628+ N2 8
2(8)
1y2 N=N
28N 2 8 N 2 5
25N25N28
6 + 1
PN25 N28 628+
12 5 2 N3
Equation (8) can be rearranged to solve for 628:
(7)
5
p25
^y -
628
(9)
28
N2
N1 28
N1
Expressions for the quantities N28 N28 as
andsue
N28/N28 can be obtained.
3
1
2 ta 1
is assumed that
N25 + N28
1
= 25 + N28
25 + N 28
==3
N3 ,
N2 + 2
N12 (R 1 + 1)
N
N2 8 (R2 -+-1)
If it
(10)
then
N 2 8 (R + 1),
(11)
where
(12)
R.1 = N2/N2
1
1
From Eq. (11) we get
1+ R1
N28
N3 =1+R
N 228
1+ R
1 + R3
N28
1+ R
N28
1
a
3
-a.
2
(13)
1
Substitution of Eq. (13) into (9) gives
$25
P28
N 25
N2
N2 5 a 3
N
3
628
1 - a y
2
I
~
j
p25 F,
(14)
28_
where
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 concentration of the fuel, a3 = a2 = a, and equation (14) reduces to the form
&
62
28
pav
25
28
- S
aY-S(16)
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 determining 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 simultaneously 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
ATOMIC
4815 BL
S CINTILLATION
PROS EBAIRD
FIG.
1
EQUIPMENT USED TO MEASURE
LA' 40 ACTIV ITY OF THE FOILS
0.002" Al
0.005" NAT. U
0.002" Al
0.005" DEP. U
0.002"AI
SLIGHTLY
ENRICHED
NATURAL
URANIUM
FUEL
FIG. 2
FOIL
528
ARRANGEMENT
MEASUREMENTS
FOR
9
within the channel at 1.60 Mev is predominantly from L40.
condition is fulfilled about a week after the irradiation.
5)
This
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 measurement. 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 calculated 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 calibration experiment which utilizes a fission counter. The main disadvantage
of the method as compared to the integral gamma counting technique developed 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
25 aMt
P(t)
- S
N3
6 28
28
1
-
P(t) F(t),
=
a 2 y(t)
(17)
which becomes
P(t)[ay(t) - S]
628 =
28
= P(t) F(t)
1
-
(18)
ay(t)
25
when 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 uranium 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
23 5
of time after irradiation divided by the number of counts measured per U
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
The
U235 fission products in a foil of the same composition as the fuel.
functions y(t) and P(t) are dependent upon many variables including the
experimental method, the irradiation time, and the exact experimental setup; however, if determined correctly, the calculated value of 628 should
be independent of the time after irradiation at which the ratio y(t) is deterThe 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
4 0 method to detercounting technique to determine functions y(t) and the La1
mine the function P(t). A gamma-counting rather than a beta-counting tech-
mined.
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 sensitive to the condition of the surface of the uranium foils, while 'gamma
counting results are not. Movement of fission products from the uranium 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)
The
Gamma-counting methods are less sensitive to foil thickness.
energies of the gammas counted in all gamma-counting methods are
great enough so that self-shielding is negligible in uranium foils several 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 capture 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 computer is used to analyze the M.I. T. data.
ATOMIC
#815 BL
SCINTILLATION
PROBE
BAIRD
FOIL
FIG. 3
BETA
S HIE LD
EQUIPMENT FOR MEASURING GAMMA
ACTIVITY OF THE FOILS
13
The integral gamma counting technique used at M. I. T. differs from
the 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 product 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:
U
138
+ n-
U
239 23m
3 d
239 + p(0.72
2 3 9 + P(1. 2 Mev) 23
> N 292.
+ P23
Mev)
p
u
(19)
The gammas associated with these beta decays have lower energies than the
maximum 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 significant fraction of the counts of the depleted foils may come from bremsstrahlung 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 enough
p
to insure a negligible contribution from the U 239 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 can
be 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.
By
reducing 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 product
activity in the three-hour cooling period. But the radiation level associated
with the rods three hours after irradiation is only about one-tenth the level
at a half-hour after irradiation.
Another advantage of using a 0. 72 Mev bias setting rather than a 1. 20
Mev 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 Fast
Fission Effect in Lattice of Uranium Rods in Heavy Water," NYO-9661
(Feb. 21, 1962).
T. J. Thompson, A. E. Profio, I. Kaplan,
[5] Weitzberg, A., J. R.2 3 Wolberg,
"Measurements of U 8 Capture and Fast Fission in Natural Uranium,
Heavy Water Lattices," Trans. ANS, 13-5, Vol. 5, #1 (1962).