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Measurements of the effective thermal neutron cross-section and the resonance absorption integral of 233th
I. Nuclear Energy II. 1957, Vol. 5, pp. 230 to 235. Pergamon Preys Ltd., London
MEASUREMENTS OF THE EFFECTIVE THERMAL NEUTRON CROSS-SECTION AND THE RESONANCE ABSORPTION INTEGRAL OF 23”Th* G. G. MYASISHCHEVA, M. P. ANIKINA,L. L. GOL’DIN,and B. V. ERSHLER Abstract-The effective thermal neutron cross-section of thorium (uth = 7.31 & 0.10 barn) and the resonance integral for thorium have been measured in a heavy-water’reactor by an activation method. Gold, indium, and uranium were used as standards. Improved values for the effective thermal neutron cross-section of indium (0th = 162 + 10 barn) and for the resonance integral of indium (RI = 2340 f 200 barn) were determined. 1. INTRODUCTION
THE effective thermal neutron capture cross-section of 232Th and the resonance absorption integral have been measured in the heavy-water research reactor of the U.S.S.R. Academy of Sciences, using gold, indium, and uranium as standards. Measurements were made in the graphite reflector of the reactor and also in a channel in the so-called “well”; i.e. a central region of the reactor containing heavy water but no uranium rods. The cross-section of thorium was found from the activity of 233Th,which, according to the literature, has a half-life of 23.3 min and emits 1.23 MeV p-particles. The B-decay of 233Th leads to the fairly long-lived (27.4 days) /?-active 233Paemitting 05 MeV /3-particles. The gold activation was measured using the /?-rays of lg8Au (halflife 2.7 days, p-energy 0.963 MeV). The number of fissions in 235Uwas determined from the P-activity of 8gSr separated from the fission products. This emits electrons of energy 1.46 MeV and has a halflife of 53 days. The activation of indium was estimated from the intensity of the b-rays from “6In (half-life 54 min), which have a complex spectrum of maximum energy about 1 MeV. To distinguish between the thermal and resonance parts of the effective crosssections, cadmium ratios were measured for all the materials studied. The agreement between the cross-sections measured in different regions of the reactor confirmed the validity of the method. In addition, the proportion of resonance neutrons in different regions of the reactor was determined from the cadmium ratio for gold. 2. METHOD
Highly dilute solutions of the nitrates of the materials were irradiated in quartz tubes containing O-3ml of solution. In each channel the specimens were located at the position of maximum neutron flux. Not more than 60 pg of thorium, O-75 mg (usually 25 pg) of gold, 8,ug of indium, or 90 mg of natural uranium were irradiated, and therefore self-shielding of the specimens could be neglected.’ To measure the effective cross-sections, a series of solutions containing thorium and the standard substance were irradiated simultaneously. The neutron fluxes were therefore the same for all specimens. * Translated by L. C. RONSON from Atomnaya Energiya 2, 22 (1957). 230
Measurementsof the effectivethermal neutron cross-section
231
Cadmium ratios were measured as follows. The quartz test-tube containing the material under investigation was put into a cadmium cylinder 10 mm in diameter, 30 mm high, and of l-mm wall-thickness. Monitors of the same material were placed about 50 cm from the main test-tube. (In the measurement of the cadmium ratio of uranium, indium was used as a monitor instead of uranium.) The activities produced by irradiation with and without cadmium were expressed in terms of the corresponding monitor activity.
FIG. l.-Apparatus for measuring the activity with an end-window counter. l-High voltage, 2%-counter, 3-specimen tray.
An irradiation time of 5-10 min was employed. After irradiation, O-1 ml of the solution was placed on a stainless steel tray and dried. The p-activity was measured with an end-window counter having a mica window of thickness 0.6 mg/cm2 in a standard geometry of about 36 per cent efficiency. Since b-particles from all the materials had fairly large and roughly equal energies, no corrections for back-scattering by the support were made. After irradiation of the uranium specimens, strontium was separated by a method described by GLENDENIN. w Amounts of up to 10 mg of carrier (SrC,O,) containing YSr were spread on a dish of area of about 1 cm 2. In this case it was thought that there might be some self-absorption of /?-particles ; however, special measurements showed that the resulting error was less than 1.5 per cent. The activities of 233Th3 lgsAu, and l161nwere measured over at least five half-lives, and the decay of %r was followed for approximately 1 month. The measured values of the activities were extrapolated to the end of the irradiation period and corrections were then made for decay during the irradiation time. 3. RESULTS
Cadmium ratios measured for thorium, gold, uranium, and indium in different channels of the reactor are listed in Table 1. The data shown in this table was obtained by averaging the results of a number of measurements.
232
G. G.
MYASISHCHEVA, M.
P. ANIKINA, L. L. GOL’DIN, and B. V. ERSHLER
The cadmium ratio for uranium in the lattice was determined from the strontium yield. Since this ratio was large in the well and reflector, no measurements of the strontium yield were made in these regions. Instead, the ratio of the total fissionproduct activities was determined. To eliminate the effect of 23gU(formed as a result of neutron capture in 23aU), these measurements were made with pure 2W. The effective cross-sections of thorium were compared with those of gold, indium, and uranium. The ratios between the direct experimental cross-sections have no simple physical meaning, since they are strongly dependent on the neutron spectrum. It is possible, however, to obtain from them values for the effective thermal neutron cross-section and the resonance absorption integral of thorium. TABLE l.-CADM~JM
RATIOSFOR THORIUM,GOLD, URANIUM,
AND INDIUM
MEASUREDIN DIFFERENT CHANNELSOF THE REACTOR Irradiation zone Material Lattice
i
/
Well
Reflector
Th
254
0.07
14.4 f
Q.2
45
15
Atl
2.38 5 O+t
9.55 f
0.2
24
hl
*aqJ
22.6 & 2.0
180
In
2.28 f
8.34 Jo 0.14
0.10
xt40
500
f
200
17.4 rfr 0.5
TABLE 2.
MEAN EFFECIIVECROSS-SECTION OF THORIUM(IN BARN)
Standard Irradiation zone
\
An
In
zqJ
\
Reflector
7.14
6.25
Well
7.06
6.19
7.38 7.65
Lattice
7.03
6.12
IO.62
For clarity, we introduce the concept of mean effective cross-section, which, as is obvious from the statement above, depends both on the neutron spectrum and on the material chosen as standard. For instance, c&. r,, designates the mean effective crosssection of thorium obtained in the reflector using an indium standard. Table 2 shows values for the mean effective cross-sections of thorium. In calculating the data of this table, the following cross-sections were used: 98.6 barnt2p3) and 145 barn(*) for the neutron capture by indium and gold, and 590 barnt5) for uranium fission. The fission yield of sQSrwas assumed to be 4.78 per cent.@) The effective thermal neutron cross-section of thorium can be calculated from the data given in Tables 1 and 2. Naturally, this value must be independent of the region of the reactor in which the specimens were irradiated, and of the standard used. The thermal neutron activation of thorium is the difference between the activation without and with cadmium. The activation of the standard materials by thermal neutrons alone can be found by a similar method.
Measurements
of the effective thermal neutron cross-section
233
As can easily be shown, the effective thermal neutron cross-section of thorium determined with gold, for example, can be calculated from the expression: RM(Au) R,(Th) e*u
= GA” R,(Th)
- 1 _ 1.
*R,(Au)
(1)
expression (I), R,(Au) and R,(Th) designate the cadmium ratios for gold and thorium measured at the point M, and o&FAu the mean effective cross-section of thorium at a point M measured with a gold standard. Values occurring in (1) are given in Tables 1 and 2. Table 3 gives values for the effective thermal neutron crosssection of thorium calculated from (1). In
TABLE 3. EFFBCTIVETHERMALNEUTRONCROSS-SECTIONOFTHOR~UMMEASUREDIN DIFFERENTREGIONS OFTHEREACTORANDRELATlVE TODIFFBRENTSTANDARD MATERIALS (IN BARN)
Reflector Well Lattice
Au
In
7.29 7.33 7.31
6.49 6.54 6.61
7.24 7.17 6.75
!_ Consider the results shown in Table 3. The cross-sections relative to gold show remarkably good agreement with one another. The cross-sections relative to indium differ by 2 per cent and are appreciably less than the cross-sections measured with gold. The lower values measured with indium are obviously attributable to inaccuracy in the cross-section value used (the cross-section of indium, 145 barn, is given with an error of -+15 barn). To unify our results, an effective cross-section of l151nof 162 & 10 barn has to be assumed. The scatter of the thorium cross-sections determined with the indium standard in different channels is probably due to impurities in the indium, different values (varying from 55 to 58 min) were regularly obtained for its half-life. Values obtained for the thorium cross-section measured with a uranium standard show the greatest scatter. The cross-section obtained by irradiation in the reflector and in the well show satisfactory agreement with each other and with the cross-section measured with gold. The cross-section value obtained in the lattice is considerably smaller. Even so, although it was obtained by correcting a large mean effective value I@62 (see Table 2), it differs from the other values by less than 6 per cent. The best values were obtained by using the gold standard. Allowing for the weighing errors of the gold and thorium specimens, the effective thermal neutron cross-section of thorium is 7.31 & 0.10 barn. This value agrees with that obtained by CROCKER.(')
The resonance
absorptionintegralforthoriumwas
RZ(Th) = RI(Au) 2.
calculatedfromthe
F
-1 Th -
. 1
expression:
234
G. G. MYASLWCHEVA, M. P. ANIKINA, L. L. GOL’DIN,and B. V. EWILER
a value 1326 f 15 barn,(‘) (So(E)%, we obtained the following values for the resonance integral of thorium (the l/u contribution to the cross-section was not calculated): Assuming for the resonance integral of gold
(88 & 5) barn in the lattice, (63 f 2) barn in the well, (59 f 6) barn in the reflector. The discrepancy between the resonance integral values in the lattice, the well, and the reflector is to be expected, since the resonance neutron spectrum is different in these regions. It is most nearly a Fermi spectrum in the lattice, but differs strongly from this form in the well and in the reflector. Unfortunately, the experimental geometry (Fig. 2) was such that even in the lattice the spectrum could differ appreciably &&;$nental
FIG. 2.-Arrangement of experimental channel in the reactor lattice.
from a Fermi spectrum. It is thus not possible to be sure that the value 88 barn for the resonance integral was obtained in a spectrum of the form: dE (nv)g dE - - . E The resonance integral of indium in the lattice, calculated similarly, is 2340 f 200 barn. Assuming that the neutron spectrum in the lattice can be thought of as consisting of two parts, Maxwellian and Fermi, the ratio between these parts can be calculated. The thermal neutron flux can be represented by nu,, where n is the neutron density, and v,, the most probable velocity of thermal neutrons at 20°C (q, = 2200 m/set). Supposing the resonance neutron flux in the lattice is a Fermi flux, we have: (nv)gdE=
Cz.
(3)
The constant C has the dimensions of a flux, and is usually called the resonance neutron flux. In standard slowing-down theory,
where q is the slowing-down density, 5 the mean logarithmic energy loss, N the number of atoms per ems, and u, the scattering cross-section.
Measurementsof the effectivethermal neutron cross-section
23.5
As is known:
dE
= 1326 barn(‘), a,, = 98*6 barn,(lr2) and (1 ” > Au RCd= 2.38 (see Table 2), we find that nv,/C = 18.5. Note. Whilst this paper was in the press, MACKLIN and POMERANCE(~) published a measurement of the resonance integral of thorium. These authors give a value (67 & 5) barn. The experiment was carried out by activating thorium in a neutron beam. Gold was used as standard, and a value 1513 barn was assumed for the resonance integral (we have assumed 1326 barn). To compare our own results with those of MACKLINand POMERANCE it is necessary to subtract from our values the I/v contribution to the cross-section and to recalculate our results relative to a gold cross-section of 1513 barn. This gives:
Substituting in (5) for gold
(96 & 6) barn in the lattice, (68 f 3) barn in the well, (64 f 7) barn in the reflector. The result (67 & 5) barn obtained by MACKLINand POMERANCE was in a beam for which the cadmium ratio for gold was 2.75. In our own case, the cadmium ratio for gold was 2.38 in the lattice and 9.6 in the well. The experimental conditions of MACKLINand POMERANCE were therefore intermediate between our conditions in the lattice and in the well, though more similar to the former. The result obtained by the two authors is almost the same as our value in the well. However, since the cadmium ratio is not fully characteristic of a spectrum, which in both cases may differ considerably from a Fermi spectrum, the reason for the discrepancy between the results cannot be stated definitely. REFERENCES L. E. NNES Plutonium Project Record Radiochemical Studies; Fission Products. 1. GLENDENIN p. 1460 (1951). 2. CARTERR. S. et al. Phys. Reo. 92, 716 (1953). 3. EGELSTAFF P. A. J. Nucl. Energy 1, 57 (1954). 4. HUGHESD. J. Pile Neutron Research Addison Wesley (1953). 5. Z. Exp. Teor. Fiz. Moscow 29,535 (1955). 6. REEDand TURKEVICHPhys. Rev. 92, No. 6, (1953). 7. CRACKERV. S. J. Nucl. Energy 1, No. 3, (1955). 8. POPOVIC D. Z. Naturforsch. 9a, No. 7-8, 600 (1954). 9. MACKLINand POMERANCEJ. Nucl. Ener;py 2, No. 4, 243 (1956).
MEASUREMENTS OF THE EFFECTIVE THERMAL NEUTRON CROSS-SECTION AND THE RESONANCE ABSORPTION INTEGRAL OF 23”Th* G. G. MYASISHCHEVA, M. P. ANIKINA,L. L. GOL’DIN,and B. V. ERSHLER Abstract-The effective thermal neutron cross-section of thorium (uth = 7.31 & 0.10 barn) and the resonance integral for thorium have been measured in a heavy-water’reactor by an activation method. Gold, indium, and uranium were used as standards. Improved values for the effective thermal neutron cross-section of indium (0th = 162 + 10 barn) and for the resonance integral of indium (RI = 2340 f 200 barn) were determined. 1. INTRODUCTION
THE effective thermal neutron capture cross-section of 232Th and the resonance absorption integral have been measured in the heavy-water research reactor of the U.S.S.R. Academy of Sciences, using gold, indium, and uranium as standards. Measurements were made in the graphite reflector of the reactor and also in a channel in the so-called “well”; i.e. a central region of the reactor containing heavy water but no uranium rods. The cross-section of thorium was found from the activity of 233Th,which, according to the literature, has a half-life of 23.3 min and emits 1.23 MeV p-particles. The B-decay of 233Th leads to the fairly long-lived (27.4 days) /?-active 233Paemitting 05 MeV /3-particles. The gold activation was measured using the /?-rays of lg8Au (halflife 2.7 days, p-energy 0.963 MeV). The number of fissions in 235Uwas determined from the P-activity of 8gSr separated from the fission products. This emits electrons of energy 1.46 MeV and has a halflife of 53 days. The activation of indium was estimated from the intensity of the b-rays from “6In (half-life 54 min), which have a complex spectrum of maximum energy about 1 MeV. To distinguish between the thermal and resonance parts of the effective crosssections, cadmium ratios were measured for all the materials studied. The agreement between the cross-sections measured in different regions of the reactor confirmed the validity of the method. In addition, the proportion of resonance neutrons in different regions of the reactor was determined from the cadmium ratio for gold. 2. METHOD
Highly dilute solutions of the nitrates of the materials were irradiated in quartz tubes containing O-3ml of solution. In each channel the specimens were located at the position of maximum neutron flux. Not more than 60 pg of thorium, O-75 mg (usually 25 pg) of gold, 8,ug of indium, or 90 mg of natural uranium were irradiated, and therefore self-shielding of the specimens could be neglected.’ To measure the effective cross-sections, a series of solutions containing thorium and the standard substance were irradiated simultaneously. The neutron fluxes were therefore the same for all specimens. * Translated by L. C. RONSON from Atomnaya Energiya 2, 22 (1957). 230
Measurementsof the effectivethermal neutron cross-section
231
Cadmium ratios were measured as follows. The quartz test-tube containing the material under investigation was put into a cadmium cylinder 10 mm in diameter, 30 mm high, and of l-mm wall-thickness. Monitors of the same material were placed about 50 cm from the main test-tube. (In the measurement of the cadmium ratio of uranium, indium was used as a monitor instead of uranium.) The activities produced by irradiation with and without cadmium were expressed in terms of the corresponding monitor activity.
FIG. l.-Apparatus for measuring the activity with an end-window counter. l-High voltage, 2%-counter, 3-specimen tray.
An irradiation time of 5-10 min was employed. After irradiation, O-1 ml of the solution was placed on a stainless steel tray and dried. The p-activity was measured with an end-window counter having a mica window of thickness 0.6 mg/cm2 in a standard geometry of about 36 per cent efficiency. Since b-particles from all the materials had fairly large and roughly equal energies, no corrections for back-scattering by the support were made. After irradiation of the uranium specimens, strontium was separated by a method described by GLENDENIN. w Amounts of up to 10 mg of carrier (SrC,O,) containing YSr were spread on a dish of area of about 1 cm 2. In this case it was thought that there might be some self-absorption of /?-particles ; however, special measurements showed that the resulting error was less than 1.5 per cent. The activities of 233Th3 lgsAu, and l161nwere measured over at least five half-lives, and the decay of %r was followed for approximately 1 month. The measured values of the activities were extrapolated to the end of the irradiation period and corrections were then made for decay during the irradiation time. 3. RESULTS
Cadmium ratios measured for thorium, gold, uranium, and indium in different channels of the reactor are listed in Table 1. The data shown in this table was obtained by averaging the results of a number of measurements.
232
G. G.
MYASISHCHEVA, M.
P. ANIKINA, L. L. GOL’DIN, and B. V. ERSHLER
The cadmium ratio for uranium in the lattice was determined from the strontium yield. Since this ratio was large in the well and reflector, no measurements of the strontium yield were made in these regions. Instead, the ratio of the total fissionproduct activities was determined. To eliminate the effect of 23gU(formed as a result of neutron capture in 23aU), these measurements were made with pure 2W. The effective cross-sections of thorium were compared with those of gold, indium, and uranium. The ratios between the direct experimental cross-sections have no simple physical meaning, since they are strongly dependent on the neutron spectrum. It is possible, however, to obtain from them values for the effective thermal neutron cross-section and the resonance absorption integral of thorium. TABLE l.-CADM~JM
RATIOSFOR THORIUM,GOLD, URANIUM,
AND INDIUM
MEASUREDIN DIFFERENT CHANNELSOF THE REACTOR Irradiation zone Material Lattice
i
/
Well
Reflector
Th
254
0.07
14.4 f
Q.2
45
15
Atl
2.38 5 O+t
9.55 f
0.2
24
hl
*aqJ
22.6 & 2.0
180
In
2.28 f
8.34 Jo 0.14
0.10
xt40
500
f
200
17.4 rfr 0.5
TABLE 2.
MEAN EFFECIIVECROSS-SECTION OF THORIUM(IN BARN)
Standard Irradiation zone
\
An
In
zqJ
\
Reflector
7.14
6.25
Well
7.06
6.19
7.38 7.65
Lattice
7.03
6.12
IO.62
For clarity, we introduce the concept of mean effective cross-section, which, as is obvious from the statement above, depends both on the neutron spectrum and on the material chosen as standard. For instance, c&. r,, designates the mean effective crosssection of thorium obtained in the reflector using an indium standard. Table 2 shows values for the mean effective cross-sections of thorium. In calculating the data of this table, the following cross-sections were used: 98.6 barnt2p3) and 145 barn(*) for the neutron capture by indium and gold, and 590 barnt5) for uranium fission. The fission yield of sQSrwas assumed to be 4.78 per cent.@) The effective thermal neutron cross-section of thorium can be calculated from the data given in Tables 1 and 2. Naturally, this value must be independent of the region of the reactor in which the specimens were irradiated, and of the standard used. The thermal neutron activation of thorium is the difference between the activation without and with cadmium. The activation of the standard materials by thermal neutrons alone can be found by a similar method.
Measurements
of the effective thermal neutron cross-section
233
As can easily be shown, the effective thermal neutron cross-section of thorium determined with gold, for example, can be calculated from the expression: RM(Au) R,(Th) e*u
= GA” R,(Th)
- 1 _ 1.
*R,(Au)
(1)
expression (I), R,(Au) and R,(Th) designate the cadmium ratios for gold and thorium measured at the point M, and o&FAu the mean effective cross-section of thorium at a point M measured with a gold standard. Values occurring in (1) are given in Tables 1 and 2. Table 3 gives values for the effective thermal neutron crosssection of thorium calculated from (1). In
TABLE 3. EFFBCTIVETHERMALNEUTRONCROSS-SECTIONOFTHOR~UMMEASUREDIN DIFFERENTREGIONS OFTHEREACTORANDRELATlVE TODIFFBRENTSTANDARD MATERIALS (IN BARN)
Reflector Well Lattice
Au
In
7.29 7.33 7.31
6.49 6.54 6.61
7.24 7.17 6.75
!_ Consider the results shown in Table 3. The cross-sections relative to gold show remarkably good agreement with one another. The cross-sections relative to indium differ by 2 per cent and are appreciably less than the cross-sections measured with gold. The lower values measured with indium are obviously attributable to inaccuracy in the cross-section value used (the cross-section of indium, 145 barn, is given with an error of -+15 barn). To unify our results, an effective cross-section of l151nof 162 & 10 barn has to be assumed. The scatter of the thorium cross-sections determined with the indium standard in different channels is probably due to impurities in the indium, different values (varying from 55 to 58 min) were regularly obtained for its half-life. Values obtained for the thorium cross-section measured with a uranium standard show the greatest scatter. The cross-section obtained by irradiation in the reflector and in the well show satisfactory agreement with each other and with the cross-section measured with gold. The cross-section value obtained in the lattice is considerably smaller. Even so, although it was obtained by correcting a large mean effective value I@62 (see Table 2), it differs from the other values by less than 6 per cent. The best values were obtained by using the gold standard. Allowing for the weighing errors of the gold and thorium specimens, the effective thermal neutron cross-section of thorium is 7.31 & 0.10 barn. This value agrees with that obtained by CROCKER.(')
The resonance
absorptionintegralforthoriumwas
RZ(Th) = RI(Au) 2.
calculatedfromthe
F
-1 Th -
. 1
expression:
234
G. G. MYASLWCHEVA, M. P. ANIKINA, L. L. GOL’DIN,and B. V. EWILER
a value 1326 f 15 barn,(‘) (So(E)%, we obtained the following values for the resonance integral of thorium (the l/u contribution to the cross-section was not calculated): Assuming for the resonance integral of gold
(88 & 5) barn in the lattice, (63 f 2) barn in the well, (59 f 6) barn in the reflector. The discrepancy between the resonance integral values in the lattice, the well, and the reflector is to be expected, since the resonance neutron spectrum is different in these regions. It is most nearly a Fermi spectrum in the lattice, but differs strongly from this form in the well and in the reflector. Unfortunately, the experimental geometry (Fig. 2) was such that even in the lattice the spectrum could differ appreciably &&;$nental
FIG. 2.-Arrangement of experimental channel in the reactor lattice.
from a Fermi spectrum. It is thus not possible to be sure that the value 88 barn for the resonance integral was obtained in a spectrum of the form: dE (nv)g dE - - . E The resonance integral of indium in the lattice, calculated similarly, is 2340 f 200 barn. Assuming that the neutron spectrum in the lattice can be thought of as consisting of two parts, Maxwellian and Fermi, the ratio between these parts can be calculated. The thermal neutron flux can be represented by nu,, where n is the neutron density, and v,, the most probable velocity of thermal neutrons at 20°C (q, = 2200 m/set). Supposing the resonance neutron flux in the lattice is a Fermi flux, we have: (nv)gdE=
Cz.
(3)
The constant C has the dimensions of a flux, and is usually called the resonance neutron flux. In standard slowing-down theory,
where q is the slowing-down density, 5 the mean logarithmic energy loss, N the number of atoms per ems, and u, the scattering cross-section.
Measurementsof the effectivethermal neutron cross-section
23.5
As is known:
dE
= 1326 barn(‘), a,, = 98*6 barn,(lr2) and (1 ” > Au RCd= 2.38 (see Table 2), we find that nv,/C = 18.5. Note. Whilst this paper was in the press, MACKLIN and POMERANCE(~) published a measurement of the resonance integral of thorium. These authors give a value (67 & 5) barn. The experiment was carried out by activating thorium in a neutron beam. Gold was used as standard, and a value 1513 barn was assumed for the resonance integral (we have assumed 1326 barn). To compare our own results with those of MACKLINand POMERANCE it is necessary to subtract from our values the I/v contribution to the cross-section and to recalculate our results relative to a gold cross-section of 1513 barn. This gives:
Substituting in (5) for gold
(96 & 6) barn in the lattice, (68 f 3) barn in the well, (64 f 7) barn in the reflector. The result (67 & 5) barn obtained by MACKLINand POMERANCE was in a beam for which the cadmium ratio for gold was 2.75. In our own case, the cadmium ratio for gold was 2.38 in the lattice and 9.6 in the well. The experimental conditions of MACKLINand POMERANCE were therefore intermediate between our conditions in the lattice and in the well, though more similar to the former. The result obtained by the two authors is almost the same as our value in the well. However, since the cadmium ratio is not fully characteristic of a spectrum, which in both cases may differ considerably from a Fermi spectrum, the reason for the discrepancy between the results cannot be stated definitely. REFERENCES L. E. NNES Plutonium Project Record Radiochemical Studies; Fission Products. 1. GLENDENIN p. 1460 (1951). 2. CARTERR. S. et al. Phys. Reo. 92, 716 (1953). 3. EGELSTAFF P. A. J. Nucl. Energy 1, 57 (1954). 4. HUGHESD. J. Pile Neutron Research Addison Wesley (1953). 5. Z. Exp. Teor. Fiz. Moscow 29,535 (1955). 6. REEDand TURKEVICHPhys. Rev. 92, No. 6, (1953). 7. CRACKERV. S. J. Nucl. Energy 1, No. 3, (1955). 8. POPOVIC D. Z. Naturforsch. 9a, No. 7-8, 600 (1954). 9. MACKLINand POMERANCEJ. Nucl. Ener;py 2, No. 4, 243 (1956).