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Resonance absorption in the power station reactor
J.
Nuclear
Energy
II, 1958. Vol. 6, pp. 345 to 350.
Pergamon
Press Ltd., London
RESONANCE ABSORPTION IN THE POWER STATION REACTOR* Z. I. GROMOVA, B. G. DUBOVSICY, A. V. KAMAEV
and V. V. ORLOV
(Received 2 November 1956) Abstract-One of the important quantities governing the conditions of a chain reaction in a uraniummoderator system is the probability (1 -p) that the fission neutrons will undergo resonance absorption during the process of slowing down. At the present day (1 -p) cannot reliably be calculated for heterogeneous reactors, so that it has to be determined experimentally. Methods of measuring it are discussed, and the corrections which must be applied for neutron leakage, uranium fission and resonance capture are considered. These corrections are substantial in the case of the power station reactor, which operates with uranium containing 5 per cent 235U. The resonance escape probability p for this reactor is calculated by three methods and found to be 0.900 rt 0.015. METHOD THE
basic experimental datum for a measurement of the resonance escape probability
FIG. 1. The neutron
balance in a reactor. U, is the leakage probability the other quantities are defined in the text.
for thermal
neutrons;
in a given reactor is the ratio R/T, where R is the number of resonance neutrons and T the number of thermal neutrons captured by 238Uper second.(i) In combination with certain other data this ratio allows p to be calculated in the following three ways. (1) Suppose that the number of fission neutrons created per cm3 set in a lattice cell be Q. Then the slowing-down density at the energy E is the product Qp(E)@(E), where O(E) is the probability that the neutron has also escaped capture in 235U, in the constructional materials, and has not leaked from the reactor. If it be assumed that O(E) varies only slowly with E, and that the absorption in 238Uessentially occurs only in the narrow interval between 6 and 200 eV, then
p
R i
Q@(g)
. (1 - p),
(1)
@(E)
being that fraction of the fast neutrons Q which is slowed down to the energy at which resonance absorption in 238Ubecomes effective (Fig. 1). The thermal-neutron-induced activation of 238Ucan be written in the form 0.4 eV
TS *
s0
(nv)U%23,(E)
dK
Translated by R. D. LOWDE from Atomnaya Energiya 2, 411 (1957). [Reprint No. AE109.1 345
346
Z. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEVand V. V. ORL~V
in which (nv), is the thermal neutron flux in the uranium and &233 is the macroscopic absorption
cross-section
of 233U. Thus
R T
Q@(E)
s
-z
@4
(N u &233(E)
0
Q is related to the thermal
-(1 - p)
neutron
(3)
dE
flux by
Q = bdS(hA~~(E) -dE}[l+ WTM where ,u is the fast neutron multiplication per fission, Xf235 the macroscopic
uranium reactors
Y the number of neutrons created
fission cross-section
of the 235U fissions that is induced the fact that a substantial
coefficient,
by epicadmium
part-between
(4)
of 235U, and
neutrons.
10 and 20 per cent-of
takes place at energies above O-4 eV.
(R/T), is that part
Equation
(4) allows for
the fission in enriched
It follows that
%a238 y$%235[1
(3
+ (W)$‘(~)
*
cross-sections for absorption in 233U and %233 and %235 here are the macroscopic fission in 235U averaged over the spectrum of sub-cadmium neutrons at the appropriate temperature (2) A
and with allowance somewhat
RADKOVSKY.‘~)
for departures
different
The number
expression of neutrons
from the l/u law.
for p has
been
ECd = 0.4 eV, the absorption limit of cadmium, is Qp@(&,). neutrons
absorbed
used
by KRASIK and
per second slowed down to energies below
in 238U is related to this quantity
The number of thermal
by
0.4 ev
Here
PCd is the probability
region
that a neutron
of energies, f is the thermal
thermal
neutron
. dE = QPWC&‘,,P
W,&233(E)
s0
absorption
coefficient,
F is that part of the Fare defined by
f and
.dE
(n%F&)
s
and
which is due to 233U.
0.4 ev
.
(6)
will not leak out of the cell in the thermal
utilization
in uranium
.
f= 00.4eV 1 W,&dE) ,O
.dE '
0.4 ev (nZ))&a238(E)
s
F=
O cl.4ev (%,&z,(E)
s0 EC,,
is the macroscopic
scopic
cross-section
materials.
absorption for neutron
Substituting
. dE dE
cross-section absorption
'
of uranium, in uranium
and Xatot is the macro-
and in the constructional
(6) in (3),
TIR
’=T/R + fWE,,Pc#W) W%3f’cdW) gives
the reduction
in the number
(7)
* of neutrons
at thermal
energy,
Resonance absorption
in the power station reactor
347
compared with the number at the energy E where the preponderant part of the resonance absorption occurs. Capture and leakage are responsible for this reduction. a(,!?) may be written in the form P(&@), in which P and x are respectively the probabilities of escaping leakage and of escaping capture by 235U and the constructional materials while slowing down to the resonance energy of 238U. x can be estimated from the known nuclear cross-sections and resonance integrals. (3) p may also be determined by comparing R/T for uranium with the value obtained for a resonance detector having a known resonance absorption integral and a known cross-section in the thermal region. Writing E, for the resonance energy dE
E for its resonance absorption
of the detecting substance and
integral,
In (8), 6 is the mean logarithmic energy loss per collision and ES is the macroscopic scattering cross-section of the moderator; (nv) is the thermal neutron flux. For uranium R QW%1 - P) (9) T = 04eV 0 238
I
0
Wh,~,,,~a,,,W
dE
’
in which N238is the number of 238Unuclei cm-3 and a,,,, the absorption cross-section of =IJ. Thus
-=-.
0
PE)
;$3
1-P
s
@4 eV (nvhJN23,%23,(E)
0
0.4
j-
dE (10)
ev
nvo,,(E) dE 0
MEASUREMENTS
The number of neutrons absorbed in 238Uwas determined from the #?-activity of 23gU as follows: =sIJ + .--+239u- 23’5min 8. Y
239Np
2.3
days+
230pU.
BY
R/T was derived from measurements on bare and cadmium-wrapped uranium, a cadmium thickness of O-25 mm being chosen to fix the effective upper limit of the absorbed range of energies at 0.4 eV. As shown in Fig. 2, the specimen consisted of a length of uranium especially inserted into a fuel rod. The sample and holder were designed to be an exact copy of the uranium fuel element normally used in the reactor, and were exposed in a hole similar to a fuel-element hole; the results for p therefore apply to the actual lattice under working conditions. Determination of R The cadmium-encased specimen was loaded into the reactor together with iodine and indium detectors which served to monitor the integrated exposure. A ten-minute
348
2. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEV and V. V. ORLOV
irradiation was then made at 1 kW, after which the material was processed chemically to purify it from fission fragments and natural decay products. The specimen was dissolved in concentrated nitric acid and two successive ether extractions performed. (Uranyl nitrate, UO,(NO,), is very soluble in ether, a fact which is also the basis of a purification method in which the nitric acid salt of uranium is recovered from aqueous solution by the addition of ether.) The ,@activity of 239U in the purified
L (a) FIG. 2. Specimens,
(b)
1
of segments of. a. fuel rod; (a) uncovered, and (b) encased m cadmium. 2-the specimen; 3-water; 4-the cadmium cover.
consisting
l-uranium;
solution was measured by a cylindrical p-counter in standard geometry. Measurements were made throughout three to four decay periods as a check on the purification procedure. Since a half-life of 23.5 min was obtained, in agreement with the figure for 239U, the purification would appear to have been entirely satisfactory. Determination of R + T The procedure described above was carried through again with an uncovered specimen, yielding a uranium solution whose activity was proportional to R + T. R/T was derived from the above results after normalising to the same integrated exposure and applying a correction for the differing amounts of uranium in the two solutions. Ten series of measurements were made in the central fuel channel of the reactor, and gave a figure R/T = 1.67 + 0.03. The quoted error is the standard deviation. Control experiments Measurements were made with a view to detecting a possible effect of cadmium thickness on the figure for p. With the experimental arrangement employed this effect was in fact negligible. A measurement at the boundary between the core and the reflector gave the value R/T = 1.2. As might have been expected, this figure is smaller than in the centre of the reactor, because the presence of the reflector enhances the thermal component of the neutron spectrum. Another measurement made in a lattice cell between two of the boron compensating rods gave R/T = 1.9. These observations serve to underline the fact that a reliable measurement of p must be made in a region where the neutron spectrum has its equilibrium shape. The central cell of the reactor is sufficiently far from the absorbing rods to satisfy this condition.
Resonance absorption
in the
power station reactor
349
RESULTS
Results obtained by taking the three methods of calculation in turn are given below. (1) Into equation (5) were inserted the following constants:
Here the first factor on the right-hand side is the ratio of the appropriate crosssections after averaging over a Maxwell spectrum for a temperature* of 500”K, while the second is the ratio of the number of nuclei cm-3. (D(E) = P(E)x(E) = 0.8.
/L= 1;
v = 246;
P(E) was calculated from the formula P(E) = exp [-K%-(E)], and K(E) was estimated from the cadmium ratio for fission capture and from the resonance integrals of the absorbing substances present in the lattice cell. (R/T)f was obtained by measuring the cadmium ratio, which came to 12, of a 235U foil exposed in the central hole of the reactor. It is found thatp = 0.906. The error in this figure is principally due to inaccuracies in the above constants and in the estimate of neutron leakage; we estimate it to be l-5 per cent. (2) Using the values
@(Ed qiF)=.
PCd= 0.955;
go5.
0
f = 0.74;
’
F = 0.108
formula (7) gives p = O-90. The good agreement between this figure and that derived from equation (5) suggests that the estimates of neutron leakage and capture have been made correctly. (3) To apply method 3 we have used a resonance detector consisting of gold. The resonance energy of gold is 4.91 eV, which is below the first level of 23sU(6.7 eV); thusp(4.91 eV) may be considered to be identical withp(0.4 eV), and in formula (lo), p(E,) can be replaced by p. The measurement of (R/T)‘38 = I.67 was taken wirh an actual fuel element so as to reproduce the working conditions of the reactor. To ensure that the cadmium ratio observed with gold maintained these conditions a foil thickness of 10 mg cmW2 was employed, which is thin enough not to distort the neutron flux. A figure (R/T), = 2 was obtained for a position in the moderator. The mean neutron flux in the fuel element is 85 per cent of that in the moderator. Thus assuming that the cross-sections of both 238U and Au follow the (I/v) law in the thermal region, the second factor in (10) should be written
o*85aa238N238
. Since
OAU E,
+
17,
Q(E)
&
(D(E,) and (10) reduces to R
1 --p
P
=
0 F
0T
* The neutron 6
temperature
238
R
.
o-85%a238N238
~guG5 Au
was measured
by E. F.
MAKAROV.
m
(11)
Z. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEVand V. V. ORLOV
350
These constants
were used:
s
dE (TaAll- = 1300; 0.4ev E 03
uA,~=95;
all values being in barns. per 23sU atom.
The agreement
us is the scattering
cross-section
between these three determinations
principles
are sound.
bility in the power station reactor
of factors
combine
enrichment
of the uranium, in the core.
and an unusual
POMERANCHUK,(~) taking -account Our methods We
are
amount
of absorption
The result agrees satisfactorily
by EGIAZAROV’~) and
of the elaborate
of dealing with the various complications
in other reactor continued
given
escape rather
high neutron leakage,
For these reasons p has not been deter-
better than I.5 per cent. formulae
of resonance
There is a comparatively
mined to an accuracy
from
escape proba-
REMARKS
materials
calculated
may be taken to indicate that
to make a measurement
due to constructional figure
expressed
is 0,900 & 0.015.
difficult in the power station reactor. a considerable
of the moderator
A mean figure for the resonance
CONCLUDING A number
F=&rs=216; 238
(1 l), p = 0.89 + O-02.
From
the underlying
~~s=2.8;
geometry
with a
by GUREVICH and of the fuel element.
may conceivably
be of interest
calculations.
greatly
indebted
to Dr.
A. K.
KRASIN for valuable
interest in the work and for assistance
also due to M. E. MINASHIN for helpful remarks,
in carrying
advice,
it through.
for
his
Thanks
are
and to the staff of the power station
for their co-operation. REFERENCES Conference of the U.S.S.R. Academy of 1. EGIAZAROV M. B., DIKAREVV. S. and MADYEEVV. G. Sciences on the Peaceful Uses of Atomic Energy, Moscow, 1955. Physical Sciences Division. English language edition p. 59. Consultants Bureau, New York (1955). 2. KRASIKS. and RADKOVSKY A. Proceedings of the International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1955. Vol. 5, p. 229. United Nations (1956). 3. GUREMCHI. I. and POMERANCHUK I. YA. Ibid. Vol. 5, p. 466.
Nuclear
Energy
II, 1958. Vol. 6, pp. 345 to 350.
Pergamon
Press Ltd., London
RESONANCE ABSORPTION IN THE POWER STATION REACTOR* Z. I. GROMOVA, B. G. DUBOVSICY, A. V. KAMAEV
and V. V. ORLOV
(Received 2 November 1956) Abstract-One of the important quantities governing the conditions of a chain reaction in a uraniummoderator system is the probability (1 -p) that the fission neutrons will undergo resonance absorption during the process of slowing down. At the present day (1 -p) cannot reliably be calculated for heterogeneous reactors, so that it has to be determined experimentally. Methods of measuring it are discussed, and the corrections which must be applied for neutron leakage, uranium fission and resonance capture are considered. These corrections are substantial in the case of the power station reactor, which operates with uranium containing 5 per cent 235U. The resonance escape probability p for this reactor is calculated by three methods and found to be 0.900 rt 0.015. METHOD THE
basic experimental datum for a measurement of the resonance escape probability
FIG. 1. The neutron
balance in a reactor. U, is the leakage probability the other quantities are defined in the text.
for thermal
neutrons;
in a given reactor is the ratio R/T, where R is the number of resonance neutrons and T the number of thermal neutrons captured by 238Uper second.(i) In combination with certain other data this ratio allows p to be calculated in the following three ways. (1) Suppose that the number of fission neutrons created per cm3 set in a lattice cell be Q. Then the slowing-down density at the energy E is the product Qp(E)@(E), where O(E) is the probability that the neutron has also escaped capture in 235U, in the constructional materials, and has not leaked from the reactor. If it be assumed that O(E) varies only slowly with E, and that the absorption in 238Uessentially occurs only in the narrow interval between 6 and 200 eV, then
p
R i
Q@(g)
. (1 - p),
(1)
@(E)
being that fraction of the fast neutrons Q which is slowed down to the energy at which resonance absorption in 238Ubecomes effective (Fig. 1). The thermal-neutron-induced activation of 238Ucan be written in the form 0.4 eV
TS *
s0
(nv)U%23,(E)
dK
Translated by R. D. LOWDE from Atomnaya Energiya 2, 411 (1957). [Reprint No. AE109.1 345
346
Z. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEVand V. V. ORL~V
in which (nv), is the thermal neutron flux in the uranium and &233 is the macroscopic absorption
cross-section
of 233U. Thus
R T
Q@(E)
s
-z
@4
(N u &233(E)
0
Q is related to the thermal
-(1 - p)
neutron
(3)
dE
flux by
Q = bdS(hA~~(E) -dE}[l+ WTM where ,u is the fast neutron multiplication per fission, Xf235 the macroscopic
uranium reactors
Y the number of neutrons created
fission cross-section
of the 235U fissions that is induced the fact that a substantial
coefficient,
by epicadmium
part-between
(4)
of 235U, and
neutrons.
10 and 20 per cent-of
takes place at energies above O-4 eV.
(R/T), is that part
Equation
(4) allows for
the fission in enriched
It follows that
%a238 y$%235[1
(3
+ (W)$‘(~)
*
cross-sections for absorption in 233U and %233 and %235 here are the macroscopic fission in 235U averaged over the spectrum of sub-cadmium neutrons at the appropriate temperature (2) A
and with allowance somewhat
RADKOVSKY.‘~)
for departures
different
The number
expression of neutrons
from the l/u law.
for p has
been
ECd = 0.4 eV, the absorption limit of cadmium, is Qp@(&,). neutrons
absorbed
used
by KRASIK and
per second slowed down to energies below
in 238U is related to this quantity
The number of thermal
by
0.4 ev
Here
PCd is the probability
region
that a neutron
of energies, f is the thermal
thermal
neutron
. dE = QPWC&‘,,P
W,&233(E)
s0
absorption
coefficient,
F is that part of the Fare defined by
f and
.dE
(n%F&)
s
and
which is due to 233U.
0.4 ev
.
(6)
will not leak out of the cell in the thermal
utilization
in uranium
.
f= 00.4eV 1 W,&dE) ,O
.dE '
0.4 ev (nZ))&a238(E)
s
F=
O cl.4ev (%,&z,(E)
s0 EC,,
is the macroscopic
scopic
cross-section
materials.
absorption for neutron
Substituting
. dE dE
cross-section absorption
'
of uranium, in uranium
and Xatot is the macro-
and in the constructional
(6) in (3),
TIR
’=T/R + fWE,,Pc#W) W%3f’cdW) gives
the reduction
in the number
(7)
* of neutrons
at thermal
energy,
Resonance absorption
in the power station reactor
347
compared with the number at the energy E where the preponderant part of the resonance absorption occurs. Capture and leakage are responsible for this reduction. a(,!?) may be written in the form P(&@), in which P and x are respectively the probabilities of escaping leakage and of escaping capture by 235U and the constructional materials while slowing down to the resonance energy of 238U. x can be estimated from the known nuclear cross-sections and resonance integrals. (3) p may also be determined by comparing R/T for uranium with the value obtained for a resonance detector having a known resonance absorption integral and a known cross-section in the thermal region. Writing E, for the resonance energy dE
E for its resonance absorption
of the detecting substance and
integral,
In (8), 6 is the mean logarithmic energy loss per collision and ES is the macroscopic scattering cross-section of the moderator; (nv) is the thermal neutron flux. For uranium R QW%1 - P) (9) T = 04eV 0 238
I
0
Wh,~,,,~a,,,W
dE
’
in which N238is the number of 238Unuclei cm-3 and a,,,, the absorption cross-section of =IJ. Thus
-=-.
0
PE)
;$3
1-P
s
@4 eV (nvhJN23,%23,(E)
0
0.4
j-
dE (10)
ev
nvo,,(E) dE 0
MEASUREMENTS
The number of neutrons absorbed in 238Uwas determined from the #?-activity of 23gU as follows: =sIJ + .--+239u- 23’5min 8. Y
239Np
2.3
days+
230pU.
BY
R/T was derived from measurements on bare and cadmium-wrapped uranium, a cadmium thickness of O-25 mm being chosen to fix the effective upper limit of the absorbed range of energies at 0.4 eV. As shown in Fig. 2, the specimen consisted of a length of uranium especially inserted into a fuel rod. The sample and holder were designed to be an exact copy of the uranium fuel element normally used in the reactor, and were exposed in a hole similar to a fuel-element hole; the results for p therefore apply to the actual lattice under working conditions. Determination of R The cadmium-encased specimen was loaded into the reactor together with iodine and indium detectors which served to monitor the integrated exposure. A ten-minute
348
2. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEV and V. V. ORLOV
irradiation was then made at 1 kW, after which the material was processed chemically to purify it from fission fragments and natural decay products. The specimen was dissolved in concentrated nitric acid and two successive ether extractions performed. (Uranyl nitrate, UO,(NO,), is very soluble in ether, a fact which is also the basis of a purification method in which the nitric acid salt of uranium is recovered from aqueous solution by the addition of ether.) The ,@activity of 239U in the purified
L (a) FIG. 2. Specimens,
(b)
1
of segments of. a. fuel rod; (a) uncovered, and (b) encased m cadmium. 2-the specimen; 3-water; 4-the cadmium cover.
consisting
l-uranium;
solution was measured by a cylindrical p-counter in standard geometry. Measurements were made throughout three to four decay periods as a check on the purification procedure. Since a half-life of 23.5 min was obtained, in agreement with the figure for 239U, the purification would appear to have been entirely satisfactory. Determination of R + T The procedure described above was carried through again with an uncovered specimen, yielding a uranium solution whose activity was proportional to R + T. R/T was derived from the above results after normalising to the same integrated exposure and applying a correction for the differing amounts of uranium in the two solutions. Ten series of measurements were made in the central fuel channel of the reactor, and gave a figure R/T = 1.67 + 0.03. The quoted error is the standard deviation. Control experiments Measurements were made with a view to detecting a possible effect of cadmium thickness on the figure for p. With the experimental arrangement employed this effect was in fact negligible. A measurement at the boundary between the core and the reflector gave the value R/T = 1.2. As might have been expected, this figure is smaller than in the centre of the reactor, because the presence of the reflector enhances the thermal component of the neutron spectrum. Another measurement made in a lattice cell between two of the boron compensating rods gave R/T = 1.9. These observations serve to underline the fact that a reliable measurement of p must be made in a region where the neutron spectrum has its equilibrium shape. The central cell of the reactor is sufficiently far from the absorbing rods to satisfy this condition.
Resonance absorption
in the
power station reactor
349
RESULTS
Results obtained by taking the three methods of calculation in turn are given below. (1) Into equation (5) were inserted the following constants:
Here the first factor on the right-hand side is the ratio of the appropriate crosssections after averaging over a Maxwell spectrum for a temperature* of 500”K, while the second is the ratio of the number of nuclei cm-3. (D(E) = P(E)x(E) = 0.8.
/L= 1;
v = 246;
P(E) was calculated from the formula P(E) = exp [-K%-(E)], and K(E) was estimated from the cadmium ratio for fission capture and from the resonance integrals of the absorbing substances present in the lattice cell. (R/T)f was obtained by measuring the cadmium ratio, which came to 12, of a 235U foil exposed in the central hole of the reactor. It is found thatp = 0.906. The error in this figure is principally due to inaccuracies in the above constants and in the estimate of neutron leakage; we estimate it to be l-5 per cent. (2) Using the values
@(Ed qiF)=.
PCd= 0.955;
go5.
0
f = 0.74;
’
F = 0.108
formula (7) gives p = O-90. The good agreement between this figure and that derived from equation (5) suggests that the estimates of neutron leakage and capture have been made correctly. (3) To apply method 3 we have used a resonance detector consisting of gold. The resonance energy of gold is 4.91 eV, which is below the first level of 23sU(6.7 eV); thusp(4.91 eV) may be considered to be identical withp(0.4 eV), and in formula (lo), p(E,) can be replaced by p. The measurement of (R/T)‘38 = I.67 was taken wirh an actual fuel element so as to reproduce the working conditions of the reactor. To ensure that the cadmium ratio observed with gold maintained these conditions a foil thickness of 10 mg cmW2 was employed, which is thin enough not to distort the neutron flux. A figure (R/T), = 2 was obtained for a position in the moderator. The mean neutron flux in the fuel element is 85 per cent of that in the moderator. Thus assuming that the cross-sections of both 238U and Au follow the (I/v) law in the thermal region, the second factor in (10) should be written
o*85aa238N238
. Since
OAU E,
+
17,
Q(E)
&
(D(E,) and (10) reduces to R
1 --p
P
=
0 F
0T
* The neutron 6
temperature
238
R
.
o-85%a238N238
~guG5 Au
was measured
by E. F.
MAKAROV.
m
(11)
Z. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEVand V. V. ORLOV
350
These constants
were used:
s
dE (TaAll- = 1300; 0.4ev E 03
uA,~=95;
all values being in barns. per 23sU atom.
The agreement
us is the scattering
cross-section
between these three determinations
principles
are sound.
bility in the power station reactor
of factors
combine
enrichment
of the uranium, in the core.
and an unusual
POMERANCHUK,(~) taking -account Our methods We
are
amount
of absorption
The result agrees satisfactorily
by EGIAZAROV’~) and
of the elaborate
of dealing with the various complications
in other reactor continued
given
escape rather
high neutron leakage,
For these reasons p has not been deter-
better than I.5 per cent. formulae
of resonance
There is a comparatively
mined to an accuracy
from
escape proba-
REMARKS
materials
calculated
may be taken to indicate that
to make a measurement
due to constructional figure
expressed
is 0,900 & 0.015.
difficult in the power station reactor. a considerable
of the moderator
A mean figure for the resonance
CONCLUDING A number
F=&rs=216; 238
(1 l), p = 0.89 + O-02.
From
the underlying
~~s=2.8;
geometry
with a
by GUREVICH and of the fuel element.
may conceivably
be of interest
calculations.
greatly
indebted
to Dr.
A. K.
KRASIN for valuable
interest in the work and for assistance
also due to M. E. MINASHIN for helpful remarks,
in carrying
advice,
it through.
for
his
Thanks
are
and to the staff of the power station
for their co-operation. REFERENCES Conference of the U.S.S.R. Academy of 1. EGIAZAROV M. B., DIKAREVV. S. and MADYEEVV. G. Sciences on the Peaceful Uses of Atomic Energy, Moscow, 1955. Physical Sciences Division. English language edition p. 59. Consultants Bureau, New York (1955). 2. KRASIKS. and RADKOVSKY A. Proceedings of the International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1955. Vol. 5, p. 229. United Nations (1956). 3. GUREMCHI. I. and POMERANCHUK I. YA. Ibid. Vol. 5, p. 466.