THE SOVIET JOURNAL OF ATOMIC ENERGY VOLUME 11, NO. 5

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ILLEGIB
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ILLEGIB
Volume 11, No. 5
May, 1962
THE SOVIET JOURNAL OF
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU
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VOLUME I
VACUUM MICROBALANCE TtCHNIQUES
, -
Proceedings of the 1960 Conference Sponsored by
The Institute for Exploratory Research
U. S. Army Signal Research and Development Laboratory
Edited by
M. J. KATZ
U. S. Army Signal Research and Development Labbratory
Fort Monmouth, New Jersey
Introduction-by
Thor N. Rhodin
Cornell University
The ptoceedings of this conference provide
an authoritative introduction to the rapidly
widening scope of microbalance methods
which is not available elsewhere in a single
publication.
The Usefulness of microbalance techniques in
the study of the properties of materials lies
in their extreme sensitivity and versatility.
This renders them particularly important in
studies of properties of condensed systems.
In addition to the historical use of-microbal-
ance techniques as a tool of microchemistry,
they have, in recent years, found extensive ap-
plication in the fields of metallurgy, physics,
and chemistry. The uniqueness of the method
results from the facility it provides in making
a series of precise measurements of high sen-
sitivity under carefully controlled conditions
over a wide range of temperature and
pressure.
This significant new volume contains papers
in three major categories. The first group of
reports deals with the general structural
features and measuring capabilities of micro-
balances. In the second group, a sophisti-
cated consideration and much needed evalua-
tion of sources of spurious mass changes
associated with microbalances is presented.
The third group describes some of the most
recent extensions in microbalance work to _
new research areas such as semiconductors,
ultra-high vacuum, and high temperatures.
These papers provide an interesting account
of advances in the application of the micro-
gravimetric method to three new and impor-
tant fields of research on the behavior of
materials.
170 pages
$6.50
PLENUM PRESS, INC. 227 West 17th St., New York 11, N.Y.
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EDITORIAL BOARD OF
ATOMNAYA gNERGIYA
A. I. Alikhanov
A. A. Bochvar
N. A. Dollezhal
D. V. Efremov
V. S. Emel'yanov
V. S. Fursov
V. F. Kalinin
A. K. Krasin
A. V, . Lebedinakii
A. I. Leipunskii
I. I. Novikov
( Editor-in-Chief)
B. V. Semenov
V.1. Vekaler
A. P. Vinogradov
N. A. Vlasov
Atroistant Editor)
A. P. Zeilrov
THE SOVIET JOURNAL OF
ATOMIC ENERGY
A translation of ATOMNAY A ENERGIY A,
a publication of the Academy of Sciences of the USSR
(Russian original dated November, 1961)
Vol. 11, No. 5 May, 1962
CONTENTS
PAGE
RUSS.
PAGE
On the Decrease of the Ion Pulse Duration and Ion Pulse Rate in a Cyclotron. N. I. V en ikov
1065
421
The Calculation of Heat Transfer in Tubes for the Turbulent Flow of Liquids with Small
Prandt1Numbers(Pr> 1, found that the ratio of the thickness of the dynamic layer to that of
the thermal layer was equal to Pr's with a reasonable degree of accuracy. The validity of applying this relation in
the case of the flow of a liquid metal (Pr 20
0
1.036
1.7
5
500
355
20
15
--
1.7
6
525
300
16
15
1.106
1.7
9
510
410
16
10
1.124
1.7
37
520
470
13
16
1.035
3.5
5
530
490
15
21
0.94
3.5
11
520
490
13
17
0.90
TABLE 3. Data of Experiments on the Enrichment of
Lithium Isotopes Carried out in a Modified Still
4?1
0 g
E
VI
g XCla g
n 014
Mean
temper-
ature in
still ?C
1-1
0
,C11. 0
p 0
0 p
,(12
'zt
Lithium level in
trays, mm
a)
a)
I-.p
a)
A T.'
first
cell
fifth
cell
eighth
cell
16
460
515
270
0
0
20
1.06
15
490
500
270
26
0
20-25
1.04
23
490
500
270
20
25
20-25
1.07
6
500
495
265
17
25
>20
1.08
16
505
515
265
17
25
>20
13
540
530
265
28
>20
>20
14
545
520
265
17
>20
>20
1.044
14
500
490
340
16
>20
>20
1.11
10(24)*
540
500
350
17
>20
>20
1.13
* Continuation of previous experiment.
25 50 75 100
Time, hours
Fig. 3. Variation of the enrichment in the isotope
Lis with time.
1082
first and eighth cells was observed, and there was poor re-
producibility of the results of the experiments with respect
to enrichment in the isotope Li6. For angles of inclination
of 3.5? we even observed a depletion in the isotope Li6
in the upper part of the still.
The severe fluctuations in metal level in the first
and eighth cells, as well as the non-uniform distribution
of the metal in the remaining cells, found after removal
of the trays from the still, are apparently to be explained
by the fact that during the operating process after a par-
ticular cell had overflowed, as a result of the good wetting
properties of the steel and the high surface tension of the
lithium, the metal quickly flowed through the apertures in
the partitions until a uniform metal level was attained in
the entire still or in its individual parts. We called this
phenomenon "siphoning" of the metal.
Thus, while the still was operating, the metal flowed
through periodically (intermittently), so that between in-
dividual experiments considerable changes in the degree of
enrichment in the isotope Li6 were observed. To ensure a
more constant metal level in the cells of the still and to
reduce the detrimental effect of siphoning, all the cells
(except the first and the fourth) were filled with packing?
rings of metal netting (30 mesh) with diameter and height
equal to 5-6 mm. Two series of experiments were con-
ducted at an apparatus inclination angle of 1.5? and a re-
sidual gas pressure of 9 microns of mercury.
In the first series of experiments the condenser tem-
perature was 265-270?C, and in the second it was 340-350?C
(paraffin was poured into the condenser instead of Dowtherm).
The metal level was measured in the first, fifth, and eighth
cells of the still.
It was found (Table 3) that the use of packing en-
sures a more uniform operation of the still; in most cases the
first, fifth, and eighth cells contained a level of metal which
was always considerable although not constant. Better results
were obtained at increased condenser temperatures (340-
350?C), which apparently is explainable by the more uniform
distribution of the metal in the condenser and the incline
troughs related to the reduced viscosity of the metal at high-
er temperatures. An isotopic analysis of the lithium samples
was carried out in a type MSL-3 mass spectrometer.
Unfortunately, no steady state was obtained in the
last experiment, and therefore the efficiency of one stage
of the still can be estimated only approximately on the
basis of an analysis of the data with respect to the kinetics
of the enrichment process.
The time required to achieve a given concentration
of an isotope in one half of the still may be calculated by
the formula [12]
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an I
t 2. 303a// r a (an 1) n] X log10 K
(a-1).L La-1
(4)
where a is the degree of separation attained in one cell (stage); n is the number of cells (in the present case n = 4
for half the still); K is the degree of enrichment achieved in the experiment (the maximum value of K is equal to an);
H is the capacity of one cell, in grams (in our case the capacity of a cell is 50 g); L is the evaporation rate in each
cell in grams of lithium per hour at the mean temperature of the experiment.
A calculation of the evaporation rate by the Langmuir-Knudsen formula for a mean experimental temperature
of 520?C and an evaporation surface in each cell of 6 ? 9 cm gives a value of L = 16.2 grams/hour.
The efficiency n of one stage is defined from the relation
logioa
11,= (5)
iogio am
where a is the degree of separation achieved in one stage of the still;am is the separation factor in the evaporation
of the lithium isotopes, equal to 1.08.
In order to determine the efficiency of one stage of the still, curves were calculated on the basis of Eq. (4) for
the variation of enrichment as a function of time for various degrees of separation achieved in a cell of the still (a
equal to 1.02, 1.03, 1.04, and 1.05), and correspondingly for various efficiencies of one stage. The calculated and
experimental (two points) data are shown in Fig. 3, from which we can conclude that the efficiency of one stage of
the still lies between the limits of 0.4 and 0.5.
LITERATURE CITED
1. N. M. Zhavoronkov et al., Khim. Nauka i Prom. 4, 4, 487 (1959).
2. A. Klemm, Angew. Chemie, 70, 1, 21 (1958).
3. G. Lewis and R. Macdonald, J. Am. Chem. Soc. 58, 12, 2519 (1936).
4. L. Perret, L. Pozand, and E. Saito, Report No. 1267, presented by France at the Second International Conference
on the Peaceful Uses of Atomic Energy (Geneva, 1958).
5. L. Love at al., Proceedings of the International Symposium on Isotope Separation (Amsterdam, 1958), p. 615.
6. D. Trauger et al., Proceedings of the International Symposium on Isotope Separation (Amsterdam, 1958), p. 350.
7. D. M. Mayer and M. Geppert-Mayer, Statistical Mechanics (Russian translation] (Moscow, IL, 1952).
8. T. Douglas et al., J. Am. Chem. Soc. 77, 8,2144 (1955).
9. F. Kelly, Canad. J. Phys. 32, 1, 81 (1954).
10. A. Brewer and S. Madorsky, J. Res. Nat. Bur. Standards, 38, 1, 129 (1947).
11. V. A. Malyusov, V. Yu. Orlov, N. A. Malafeev, N. N. Umnik, and N. M. Zhavoronkov, Khim. Mashinostroenie,
4, 4 (1959).
12. S. I. Babkov and N. M. Zhavoronkov, Dokl. AN SSSR, 106, 5, 877 (1956).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover- to.
cover English translations appears at the back of this issue.
1083
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LETTERS TO THE EDITOR
INVESTIGATION OF THE REACTION Be9(d, t)Be9
V. I. Serov, V. A. Pereshivkii, M. F. Andreev,
and I. K. Aver'yanov
Translated from Atomnaya Lergiya, Vol. 11, No. 5,
pp. 440-442, November, 1961
Original article submitted May 8, 1961
The reaction Be9(d, t)Bes has been studied by a number of workers [1-4]. Nevertheless, detailed studies have
not been performed for deuteron energies in the range 1.4 to 4.0 Mev. In this work measurements have been made
Fig. 1. General scheme for the arrangement of the tar-
get, spectrometer, and detectors. 1) Magnet chamber;
2) rotating section of the spectrometer chamber; 3) vacu-
um seal; 4) stationary section of the spectrometer clim-
ber; 5) cover made of plexiglass; 6, 9, 10, 14) arrange-
ment for the regulation of the position of target, dis-
phragm, etc.; 7) generator discharge pipe; 8) target; 11)
beam current measuring electode; 12) traveling dia-
phragm; 13, 19) electrodes for suppressing secondary
emission; 15) Cs! crystal; 16) light transmitting tube;
17) photomultiplier; 18, 21) leads for the set adjust-
ment of the integrators; 20) leads for secondary emis-
sion suppressing electrodes; 2) source for calibrating
the apparatus.
1084
100
.90
80
70
60
g
40
30
20
10
1
P
I 9 i
Be (d,e,
,
8e9(dpt)Li
7
r
r
1
i
' -8etd,t)Beel
1
,
5
10
15 20
25 30
35 40
Channel number
45
be?
50
Fig. 2. Momentum spectrum amplitude of particles passing
through the magnetic spectrograph.
on the differential cross section for triton production. We
have considered the dependence of the differential cross-
section for primaries scattered through 17? on deuteron
energy over a range of 1.125 to 3.8 Mev, and in this energy
range we have examined the angular distribution from 0
to 150?.
The experiment was carried out using an electro-
static generator. Deuterons are directed through a dia-
phragm 4 mm in diameter and then into the magnetic
spectrometer chamber. In the center of this a foil with a
layer of beryllium (density 100 to 150 ug/cm2) was situated.
The deuteron current was measured by an integrator when
the deuterons are all stopped in the foil, or by an insulat-
ed electrode adjusted in the path of the beam and lying
behind the target. The secondary particles emitted from
the target were analyzed in a magnetic spectrograph using
nonhomogeneous magnetic fields. Using this spectro-
meter it was possible to analyze tritons with energies up
to 5.4 Mev. For those cases in which tritons were produced
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with large energy a foil was adjusted behind the target to retard them. A general arrangement of the apparatus is
shown in Fig. 1.
To obtain measurements of the angular distribution, the spectrometer was rotated relative to an axis which
passed through the center of the target. The particle detector was a thin crystal of CsI used in conjunction with a
d6
d S2
1.5
1.0
0.5
0
00
0
1,16' 1,37
225
1.0 2.0 3.0
40 Ed,Mey
Fig. 3. The differential cross section for tritons produced from the
reaction Be9(d, t)Bes as a function of deuteron energy plotted in rela-
tive units.
photomultiplier. In order to determine the type of particle the momentum spectrum was recorded in a 50 channel
pulse height analyzer. The spectral amplitude as a function of momentum for particles emitted from the target in
a fixed magnetic field is shown in Fig. 2. The particle path for a given deuteron energy was determined by sum-
ming over the channels and then graphically integrating the curve as a function of the number of points read in the
magnetic field.
In Fig. 3. the differential cross section for triton production is displayed as a function of deuteron energy. Super-
imposed on the smooth development of the curve we note resonances at deuteron energies of 1.37 and 2.85 Mev. in
addition, we obtained a total cross section for the tritium
reaction for deuteron energies of 305 to 1480 key by
measuring the absorption of tritium in the target substrate.*
The curve illustrating these results is given in Fig. 4.
O./ Comparison of Figs. 3 and 4 seems to indicate that there
is another resonance for deuteron energy of 1.16 Mev.
Both measurements and calculations for the angular dis-
tribution for deuteron energies of 1.4, 2.5, and 3.5 Mev
0.0 are shown in Fig. 5. The calculations were made using
Butler's theory of knock-on (d, t) reaction without account-
ing for coulomb interactions. The magnitude of the or-
bital angular momentum, In, of captured neutrons in the
absorption calculations was taken equal to one. Good
05
1.0
1.5 EdPIev
Fig. 4. The total cross section for triton yield as a fun -
tion of deuteron energy for the reaction Be9(d, t).
'The work in measuring the path and the absorption of
the tritium was performed jointly with B. Ya. Guzhov-
skii.
1085
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Reaction
Eres
Energy level
Reaction
Eres
Energy level'
13e? (n, a) He?
Be? (p, n)B9
Be? (d, l)Ues
Be? (a, n)
2.6
2.3
2.33
2.75
2.43
Bo' (p, y)B19
Be? (d, f) Be'
Be' (a, it) Ci?
3.14
>3.10 ,
3.08
} 3.04
a
"8
0 9
8
0 7
E 6
0
5
3
agreement between calculation and experiment (for example
Fig. 5) is achieved if the radius of the interaction is taken as
ro = 4 ? 10-13 cm for Ed = 1.4 Mev and ro = 5 ? 10-13 cm for
Ed = 2.5 and 3.5 Mev. This does not contradict the work in
[5, 6].
The resonances in the cross section are due to bound
levels of the B compound nucleus. The excitation energies
of these levels are 16.77, 16.93, and 18.11 Mev.
Using the differential cross section (angular distribution)
it was found that the total cross section for triton production
for the studied reaction was 60 10 mbarns. At this point
it is interesting to note that there seems to be an important
correlation between the thresholds of the inelastic interactions
and the position of certain resonances in the reactions of Be9
with neutrons, protons, deuteronstand a-particles.
20 In the table given above data taken from the present
work and from [4] are cited to establish this correlation.
Analogous effects are observed in reactions involving
other light nuclei (Li7 and B10). The deductions that can be
made from these facts are that the compound nuclei formed
in the reactions of these light nuclei with excitation energies
appropriate to the indicated resonances have similar con-
figurations. The original excitation is taken to be the target
nucleus plus the incoming particle.
The authors wish to convey thanks to V. A. Ivanov and his group for providing clarity to the workings of the
electrostatic generator and also to V. Kuzyanov for assistance in taking measurements.
LITERATURE CITED
1. P.. Smither, Phys. Rev. 107, 196 (1957).
2. M. Jua, Phys. Rev. 98, 85 (1955).
3. R. Heft and W. Libby, Phys. Rev. 100, 799 (1955).
4. F. Ajzenberg-Selove and T. Lauritsen. Nucl. Phys. 11, 1, 1 (1959).
5. H. Newns, Proc. Phys. Soc. A65, 916 (1952).
6. N. A. Blasov and A. A. Ogloblin, JETP, 37, 54 (1959).
40 6'0 80 100 120 140
in cm system, deg
Fig. 5. The angular distribution of primary tritons
from the reaction Be (d, t)Be. The experimental
points are plotted using the following key for deu-
teron energy.) 0) 1.4; ,6,) 2.5; +) 3.5;
1.403 [2]; - - -) calculated using Butler's theory.
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover- to-
cover English translations appears at the back of this issue.
1086
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CROSS SECTIONS OF INELASTIC INTERACTION
OF FISSION SPECTRUM NEUTRONS
G. N. Lovchikova and 0. A. Sal'nikov
Translated from Atomnaya fnergiya, Vol. 11, No. 5,
pp. 442-443, November, 1961
Original article submitted May 27, 1961
The source of fission neutrons was a converter, which was placed in a stream of thermal neutrons leaving the
reactor and which consisted of an aluminum box containing the mixed oxide of Um with 75% enrichment. The con-
verter was placed at an angle of 45? to the direction of the thermal neutron beam. The detector was placed at a dis-
tance of 30 cm from the center of the converter.
The neutrons were recorded by a multielecaode ionization fission chamber with U238, having a spherical housing
of diameter 22 mm with a cylindrical space inside. The amount of material applied to the electrodes was 40 mg; the
U238 was depleted 100 fold, i.e., there was 100 times less
U235 than in the natural mixture of isotopes. The chamber
Cross Sections of Inelastic Reaction of Fission Spectrum was surrounded by a 0.5 mm thick cadmium cover for
Neutrons Leading to a Loss in Energy by Neutrons to a protection against thermal neutrons. The effective thres-
hold of the detector for the neutrons of the fission spec-
trum was 1.4 Mev.
Value Less Than the Fission Threshold of U238
Element
N ? 102?,
number
of atoms
in cm3
au.,
b
T
a. >,b
in
Sodium
254.3
2.0
0.037
0.47 ? 0.08
Potassium
133.1
2.3
0.981
0.47 ? 0.11
Strontium
180.0
3.1
0.950
0.93 ? 0.08
Barium
163.7
3.8
0.933
1.36 ? 0.10
Molybdenum
639.9
3.0
0.727
1.54 ? 0.03
Niobium
176.7
3.2
0.883
1.44 ? 0.08
Iron
845.8
2.2
0.807
0.73 f 0.04
The diffusers were materials consisting of a natural
mixture of isotopes. All specimens except niboium were
cast. The niobium was used in the form of a powder. The
diffusers were split hollow spheres consisting of equal halves.
The dimensions of the internal space corresponded to the
dimensions of the detector. The external diameter of all
diffusers was 90 mm.
The transmission T1 was measured, i.e., the ratio
of the count rates of the fission spectrum neutrons in the
presence of a diffuser and without it. Therefore,
where N1 is the number of counts of the detector corresponding to neutrons with the initial energy (without a diffuser);
N2 is the number of counts of the detector (with a diffuser).
The difference between the values N2 and N1 is caused by all the processes leading to discarding the energy of
the neutrons below the fission threshold of the detector. The value of transmission therefore depends in the first place
on the cross sections of inelastic scatter, capture and cross sections of other reactions which can cause disappearance
of neutrons or a high loss in energy. The main role is played by inelastic scatter since an analysis of experimental
data on the capture cross section in the region of energies 1-14 Mev for the elements in which we were interested [1]
showed that all cross sections were within the limits 1-10 mb. The threshold of reaction (n, 2) is about 5 Mev, the
cross section for most elements near a threshold of the order of 10 mb, in some cases reaching 100 mb with a neutron
energy of 14 Mev. The cross section of other reactions, for example (n, a); (n, 2n) with a neutron energy of 14 Mev,
is of the same order, only the threshold of these reactions is much higher pl. The cross section of inelastic scattering
therefore makes the main contribution to the total cross section which we found.
The cross sections for transmission were calculated by a method developed in [2]. Geometrical corrections and
corrections for the absorption of neutrons in the detector showed much lower experimental errors and were therefore
not introduced into the final calculation of the cross sections. The correction for energy losses in elastic collisions
was not considered since the final result included cross sections of all processes leading to loss in energy by neutrons
1087
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to a value less than the fission threshold of Um. It is clear that corrections such as those for fission in the detector
under the action of y -quanta and the generation of photoneutrons in the diffuser are small and can be neglected.
The neutron background was determined experimentally. Owing to the high fission threshold of U238 it was
insignificant.
The results of the measurements are given in the table. All cross sections, except those of iron, have not yet
been published in the literature and are given here for the first time. Iron was chosen to compare our data with those
of other authors. The cross section obtained for iron was 0.73?0.04 b,and within the limits of statistical errors it
agrees well with the cross section of inelastic scattering of fission spectrum neutrons equal to 0.686 I 0.043 b,
obtained for iron in [2].
A consideration of the experimental results shows that the cross sections increase with the atomic number.
LITERATURE CITED
1. An Atlas of Effective Neutron Cross Sections of Elements. Edited by D. Hughes. Moscow, Acad. Sci. USSR Press
(1955).
2. H. Bethe, J. Beyster, and Carter, J. Nucl. Energy, 3, 207 (1956); 3, 273 (1956); 4, 3 (1957); 4, 147 (1957).
ANGULAR DISTRIBUTION OF IRON-SCATTERED y -
RADIATION FROM A PLANE, MONODIRECTIONAL
Co" SOURCE
A. V. Larichev
Translated from Atomnaya inergiya, Vol. 11, No. 5,
Pp. 443-445, November, 1961
Original article submitted March 13, 1961
There have been papers [1, 2] devoted to the experimental study of the angular distribution of y -radiation from
an isotropic Cow point source in a semi-inifinite medium. Similar results from experiments with parallel beams of
8-10 Mev bremsstrahlung radiation and 1.25 Mev Co60 radiation
have been reported [3, 4].
The results for the spectral distribution of y -radiation
in an infinite medium as calculated by the moments method
have been presented [5].
The angular distribution of y -radiation from a plane,
monodirectional Co60 source which is scattered in a plane iron
slab is given in this paper.
The experimental method has been described previously
[4]. The spectra were taken with a total absorption spectro-
meter having a Nal (Ti) crystal 80 mm in height and dia-
meter.
.4
43 to3
< 7 '
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6
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111111.1111111.111111.111111
200 400 660 800 1000 1200 1400E, key
Fig. 1. Energy spectra for y -radiation scattered
at angles of 20, 50, and 70?.
1088
The pulse height distribution was worked out by means
of data for the spectrometer sensitivity function [6]. The
spectral distribution of y -radiation scattered in an iron slab
six mean free paths thick (15.6 cm) at angles of 20, 50,and
70? is shown in Fig. 1.
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The relative angular intensity distribution (relative to the intensity of unscattered radiation) of scattered radia -
don per unit solid angle is shown in Fig. 2 for three slab thicknesses. These curves are similar to curves shown in (1).
Fig. 2. Relative angular intensity distribution of scattered radiation for various slab
thicknesses: 0) 64 ox; 0) 4?0x; A) 2 Lox.
The outermost points of the curves (those for small angles) were obtained on the assumption that the dependence of
scattered radiation intensity per unit solid angle on angle is exponential, i.e.,
1(0) = /(0)exp( --0/00).
10 4
101
0 10 20 30 40 50 60 70 8 degrees
Fig. 3. Dependence of I(0) on 0 in the range
10-700 for various slab thicknesses. (For mean-
ing of symbols, see Fig. 2.)
250401
S200
iu 150
\-.C4
3 100
50
1111111
0 10 20 30 40 50 60 704 degrees
Fig. 4. Angular dependence of the intensity of
radiation scattered in the solid angle element
2/r sin 0.O for three slab thicknesses. (for mean-
ing of symbols, see Fig. 2.)
The values of 1(0) were obtained from the experimentally known quantities 1(0), 0, and O. The dependence
of I(8) on 0 is shown in Fig. 3 on a semilogarithmic scale. The dependence of scattered radiation intensity in the
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BE
6
5
4
3
2
solid angle element 27r sin OA on angle is shown in Fig. 4 for three barrier
thicknesses. A maximum in the interval from 20 to 30? is characteristic for
all three thicknesses. The total scattered radiation intensity was deter-
mined by graphical integration of the curves in Fig. 4. The dependence of
the scattered radiation build-up factor BE on slab thickness u ox is shown
in Fig. 5. The solid line was drawn through build-up factor values taken
from [7] (a Monte Carlo calculation). These values lie outside the limits
of experimental error. However, the data in [7] has an error of -.657 itself;
therefore the agreement between experimental results and the results in the
paper mentioned can be considered to be satisfactory.
LITERATURE CITED
1. G. Whyte, Canad. J. Phys.,33, 96 (1955).
1 2 3 4 5 "lox 2. Yu. A. Kazanskii, Atomnaya gnergiya, 5, 432 (1960).
3. J. Hubbell, E. Hayward, and W. Titus, Phys. Rev.,108, 1361 (1957).
Fig. 5. Comparison of experimental
and theoretical [7] values for energy
4. E. L. Stolyarova et al., ."Instruments and methods for radiation analy-
sis" Collected Scientific Papers of MIFI (Moscow, Gosatomizdat,
build-up factor.
(1961), No. 3.
5. H. Goldstein and J. Wilkins, Calculations of the Penetration of Gam-
ma-rays. US. AEC, No. 40/3075 (1954).
6. A. V. Larichev and G. A. Chervatenko, "Instruments and methods for radiation analysis" [in Russian] Collected
Scientific Papers of MIFI (Moscow, Gosatomizdat, 1961), No. 3.
7. M. Berger and J. Doggett, J. Res. Nat. Bur. Standards, 56, 2 (1956).
THE EFFECT OF THE RESONANCE STRUCTURE OF CROSS SECTIONS
ON THE PROPAGATION OF FAST NEUTRONS IN IRON
M. N. Nikolaev, V. V. Filippov, and I. I. Bondarenko
Translated from Atomnaya gnergiya, Vol. 11, No. 5,
pp. 445-447, November, 1961
Original article submitted March 23, 1961
Until recently, in the calculation of fast reactors systems of multigroup constants were used, compiled on the
basis of data on the mean cross sections [1, 2]. This method of calculating group parameters is reliable if the cross
sections within the limits of the energy group are sufficiently smooth energy functions. If a resonance structure appears
in the cross sections, then when compiling multigroup constants it is essential to consider the resonance blocking of
the cross sections. Until now this has usually only been performed in the region of isolated resonances when calcu-
lating group cross sections of radiation capture and fission for heavy nuclei [3, 4]. When calculating group para-
meters such as the coefficient of fusion (or the transport cross section corresponding to it) and the moderation cross
section, the influence of resgnance effects was neglected! However, the effects connected with the blocking of
resonances can have an important effect on these values also, which was mentioned in [6] where an allowance was
made for the resonance blocking in the compiling of a multigroup system of constants for U238 (see also [7]). As can
be seen from the results of these papers, even for such a heavy nucleus as uranium and comparatively high energies
(several tens of kiloelectron volts) the resonance blocking has a noticeable effect not only on the capture cross sec-
tion but also on the transport cross section.
* The effect of resonance blocking on the neutron moderation cross section for heavy nuclei in the region of isolated
resonances was described in [5].
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For medium weight nuclei the resonance structure of the cross sections appears up to energies of the order of
several megaelectron volts. It might therefore be supposed that for such nuclei the effect of blocking of resonances
will be important over the whole energy region ,which is of interest for reactor physics. This conclusion is confirmed
by experimental data [6].
As follows from [7], the diffusion coefficient and the neutron moderation cross section for a certain energy group
are determined (with low capture) in the following way:
I.
Eu/I\'
\f/
(1)
where p is the mean cosine of the angle of scattering; t is the mean logarithmic energy loss; Eu and E1 are the upper
and lower boundaries of the group; Z is the total macroscopic cross section, equal to the scattering cross section with
the assumption made. The brackets indicate averaging for the energy group considered.
The information which is available at the present time on resonance parameters in the region of fast neutrons
is insufficient for calculating the values of and with the required accuracy. We also notice that these
values are strongly affected by interference effects which have not
been studied at all in this energy region. In this connection it is of
interest to directly measure the values , and other
similar characteristics.
Experimental layout
We will consider the transmission T(t) of neutrons uniformly
distributed in the range of averaging of AE:
The area under the transmission curve is equal to the mean
/ 1 \
length of free path
co
1 dE /I\
T
6
Double integration of the transmission curve gives the mean square of the path length;
CO
r IC dE /I\
dt T (t')dt' =
b t AE
(2)
(3)
(4)
The mean values can also be determined in a similar way from the higher powers of 1/E.
If in expression (2) we remove exp < E > t] from the integral sign and expand the remaining expression into
a Taylor series and integrate terrnwise, we then obtain
T (t)=e?a)1[1-1-(12) 21 and evaluate the dispersion of cross section ?2.
The apparatus with which the transmission curves were measured is shown in the figure. The source of neutrons
was the reaction T (p, n)He3. Protons accelerated by an electrostatic generator impinged an tritium-titanium tar-
get 1; its thickness was about 100 key. The measurements were made at an angle of 00 to the proton beam. The
neutrons, emitted from the target and passing through the diffuser 2 without collision, through the collimator 3 in the
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Results of Treatment of Experimental Data
En, kev
.
b
1 ,
,

b
Dtrue/D

2
ri/r I '

b

b
and .
The mean cross sections which we obtained are 10-20% higher than the figures given in the atlas of D. Hughes
En This difference can be explained if the experiments, the results of which are given in the atlas, used a diffuser
with a thickness of about one path length. From the data of the table it can be seen that for the calculation of the
mean path and the mean square of this length cross sections should be used which are much smaller than
the mean cross section . The resonance blocking has a particularly important effect on the coefficient of dif-
fusion. The sixth column gives the ratios of the diffusion coefficient calculated from formula (1) to the value
1/3 (1?p)( ); even at energies of about 1.5 Mev these values differ by 50%. In the seventh and eighth columns
there are the relative dispersions of the cross section and the path lengths. Of interest is the fact that at an energy
of about 1800 key the dispersion of the cross section is very small whereas the dispersion of the path length is large.
This points to the fact that in the energy range considered the cross section has one or several fairly deep and narrow
dips, between which it does not undergo strong fluctuations. Since the dips are narrow they do not have a noticeable
effect on the value of the mean cross section. However, the presence of dips in the cross section has a strong effect
on the mean path length. It might be expected that the observed fact is characteristic for the region of almost over-
lapping resonances where, due to the geometrical limitations and the phenomenon of "repulsion" of the level, the
cross section cannot have sharp peaks. The dips in the cross section caused by random fluctuations in the density of
the levels can also occur in this energy region.
The results given are preliminary. At the present time more detailed measurements are being made of the
mean cross sections and path lengths of neutrons for a number of medium weight nuclei.
LITERATURE CITED
1. I. V. Gordeev, D. A. Kardashev, and A. V. Malyshev, Reference Book on Nuclear Physical Constants for the
Calculation of Reactors [in Russian) (Moscow Atomic Energy Press, 1960).
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2. W. Levenstein and D. Ockrent, Transactions of the Second International Conference on the Peaceful Use of
Atomic Energy (Geneva, 1958). Selected Reports of Non-Soviet Scientists [in Russian] (Moscow, Atomic Energy
Press, 1959), Vol. 3, p. 261.
3. I. V. Gordeev, V. V. Orlov, and T. Kh. Sedernikov, Atomnaya Energiya, 3, 9, 252 (1957).
4. W. Roach, Nucl. Sci. and Engng, 8, 621 (1960).
5. S. B. Shikhov and A. P. Abagyan, Collection: "The theory and methods for calculating nuclear reactors."
(Moscow, State Atomic Energy Press) (in press).
6. A. I. Leipunskii et al. Atomnaya Energiya, 5, 2, 277 (1958).
7. A. A. Luk'yanov and V. V. Orlov, Atomnaya Energiya, 10, 3, 262 (1961).
8. D. Hughes, An Atlas of Effective Neutron Cross Sections of Elements [Russian translation] (Moscow, Acad. Sci.
USSR Press, 1955).
AN EXPERIMENTAL STUDY OF A LINEAR ACCELERATOR
WITH AN ELECTRON PRE-BUNCHER
G. I. Zhileiko and D. A. Yakovlev
Translated from Atomnaya Energiya, Vol. 11, No. 5,
pp. 447-449, November, 1961
Original article submitted May 27, 1961
A simplified diagram of the device is shown inFig. 1. The high-frequency power is fed to a double resonator pre-
buncher (more accurately, an electron cluster-former) through a cable to which phase changers are connected. By
means of the phase changers the phase of arrival of the elec-
tron cluster to the accelerator is changed, which ensures that
the instant of injection of the cluster into the accelerator coin-
cides with the equilibrium phase. In the feed circuit of the
gridless resonators of the pre-buncher there are (not shown on
Phase changers
the diagram) attenuators and devices permitting remote switching
on and off of the supply to the resonators, with the accelerator
Accelerator Electron operating.
gun
Wave guide
Resonators
Fig. 1. Block diagram of accelerator with elec-
tron pre-buncher.
The studies were carried out with single resonator and
double resonator pre-bunchers.
Figure 2 shows typical dependences of the width of the
spectrum of accelerated electrons AU and the beam current at
the outlet of the accelerator on the value of the phase of high-
frequency oscillations, led only into one resonator, close to the accelerator (single resonator pre-buncher). Figures 3
and 4 illustrate the dependences of the width of the spectrum and the beam current on the injection voltage U1 on
the electron gun and the high-frequency power Pres fed into the resonator.
For a double resonator pre-buncher Figs. 5 and 6 give curves showing the dependence of the width of the spec-
trum and the beam current on the phase of oscillations cp2, fed into a resonator which is at a distance from the ac-
celerator, and the injection voltage. The systems of both resonators are chosen from the point of view of their best
mutual operation.
On the basis of the experimental data the following conclusions can be drawn:
1. The pre -buncher effectively acts on the operating system of the accelerator, the experimental dependences
being well-explained theoretically. In fact, it can be seen from the curves of Fig. 2 that for 9 = 20-40?, the electron
cluster from the pre-buncher enters the accelerator with the equilibrium phase: here the spectrum width is a mini-
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mum and current is a maximum; the phase of the phase changer cp = ?(80-1200) corresponds to the cluster entering
the region of phases of the traveling electromagnetic wave, where the conditions of bunching are the worst observed.
AU, I, relative units
12
10
8
6'
4
AU
AU
/vi/p
"Le..
200 180 120 80 40
0 40 80 120 16'D 200
Fig. 2. Dependences of width of spectrum of ac-
celerated electrons and the beam current on the value
of the phase at which the electron cluster is fed into
the accelerator: U = AU(cp); I = I() with a single
resonator pre-buncher; AUw/p = AUwip(v); 11 =
lw/p (co) without a pre-buncher.
dtf; I, relative units
2
d U
Fig. 3.
of spectrum and beam cur-
rent on voltage at which
electrons are injected into
single resonator pre-buncher.
35
45
, kv
Dependence of width
1094
illy, relative units
????11.
2
P
res' relative units
3
Fig. 4. Dependence of
width of spectrum and
beam current on the
high-frequency power
fed into the single
resonator pre-btmcher.
dU; I, relative units
10
Auw ip
AU
/ \
1
II
\
/
k
/
\I
? 1 i p_
_
1
40
120
P;
Fig. 5. Dependences of width of
spectrum and beam current on the
phase of oscillations fed into the
second resonator of the double
resonator pre-buncher from the
accelerator. Straight lines: the
same, without pre-buncher.
LIU; I, relative units
10
30 40 50
Uu, kv
Fig. 6. Dependences
of width of spectrum
and beam current on
the voltage at which
electrons are injected
into the double reson-
ator pre-buncher.
2. The use of a pre-buncher, even a single resonator
type, triples the beam current and reduces the spectrum
width to a third or a quarter.
3. A double resonator pre-buncher considerably in-
creases the beam current but there is a sharp increase in
the criticality of the operating conditions of the accelerator
(injection voltage, etc.) and the choice of the conditions
of the resonators for mutual operation is complicated.
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ONE ACCURATE SOLUTION OF A NONSTATIONARY
ALBEDO PROBLEM
T. Kh. Sedel'nikov
Translated from Atomnaya Energiya, Vol. 11, No. 5,
pp. 449-450, November, 1961
Original article submitted May 27, 1961
We will consider a homogeneous isotropic elastically-diffusing half-space. To solve the problem of finding
the outgoing flux intensity of neutrons as a function of the time we will write the corresponding albedo equation.
The latter can be obtained by formal transfer from a nonstationary kinetic equation with zero initial conditions
to a stationary equation,using the Laplace transform. The neutron capture cross section then changes formally:
Ec 2c+Piv, (1)
where p is the Laplace transform parameter; v is the speed of the neutron.
From the stationary kinetic equation we can transfer to the corresponding albedo equation [1, 2] for the intensity
of the outgoing flux I (A, ii
( 1te) dri x [
OA, 110[. -
41(? -1- + 2n I , ?0) dpi
where x0 is the cosine of the angle of incidence of the neutron; it is the cosine of the angle of exit of the neutron;
?
A=
Is +lc+ PI?
Es is the neutron scatter cross section.
A nonstationary albedo equation can also be obtained on the basis of the invariance principle [1-3]
1
Z, ?
= dt' [ (t?t')-1-2n \ I (t?t' , , tto) die] X [ 8 (I' )+27tp, (t' 11' le)
(2)
(3)
(4)
Transforming it with respect tot according to Laplace,we again obtain equation (2). Equation (2) can be used to find
an accurate expression for the total intensity of the outgoing flux for an isotropic incident flux A0(p) [1]
A0(p)=(1-171?A)/(1-1-V1?A).
Substituting expression (3) for A. we find the original of the Laplace transform
(5)
(6)
To allow for the moderating neutrons (multiplying half-space) we should proceed from a kinetic equation with
moderating neutrons
1 (3(D 0(D 1 E v
(1) = -2- [ s ?13) Et) (Do-PI Cdvii
(7)
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+I
OC;
(N(t, z) = (1) (t , z,
at
21
(8)
Here v is the number of secondary neutrons per fission; El- is the fission cross section; j is the fraction of the i-th
group of moderating neutrons; Xi is the constant of decay of the i-th group; q is the density of the nucleus-precursor
of the i-th group;
Transforming the equation with respect tot according to Laplace for zero initial conditions and excluding Ci,
we find:
act) )]
w (Ec-1- zsd-Ef +P/o) zsd-vzi P
1
This equation leads to an albedo equation (2) where A will have the form:
E,H-vli (1?p
Arno&
Is+Ec-Flf + Ply
where
The isotropic albedo is expressed as previously by formula (5) but with a new value A = Amod.
If we only consider one group of moderating neutrons, we can find analytically the original Ao(p):
+BS
Innodt) = /
' x x y
,-2 vt
4 V X
11(213 s (t ?s) ) x x+2Y1.+xt x4-1
(? vs )X exptos
(t ? 1 2 2 t; x ds,
B= I/ 11- ( ? kx+Y) ?
x x '
==lcd-Zs+It;
y=l3vZi. ?
(9)
(10)
(12)
LITERATURE CITED
1. V. A. Ambartsumyan, E. R. Mustel', A. B. Severnyi, and V. V. Sobolev, Theoretical Astrophysics [in Russian]
(Moscow, State Technical Press, 1952).
2. V. V. Sobolev, Radiant Energy Transfer in the Atmospheres of the Stars and Planets [in Russian] (Moscow, State
Technical Press, 1956).
3. Sh. Chandrasekar, Radiant Energy Transfer [Russian translation] (Moscow, Foreign Literature Press, 1953).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover- to.
cover English translations appears at the back of this issue.
1096
L
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SOME PHYSICAL PROPERTIES OF A LAYER OF ARTIFICIAL
GRAPHITE PARTICLES
Z. R. Gorbis and V. A. Kalender'yan
Translated from Atomnaya Energiya, Vol. 11, No. 5,
pp. 450-454, November, 1961
Original article submitted March 28, 1960
The use of a moving layer of graphite particles as a coolant is of interest for nuclear power. However, for this
purpose it is essential to know the basic physicomechanical and thermophysical properties of the layer of graphite par-
ticles. The material which we investigated was graphite scrap from the Zaporozh (batch 1) and Novocherkassk (batch
2) electrode plants. The ash content in the particles did not exceed 0.510. The dimensions of the particles are given
In Tables 1 and 2.
Density and Weight of One Cubic Meter of Dry Granular Graphite Particles
The mechanical and thermophysical properties of free-flowing materials are determined by the porosity of the
layer (8) or the density of packing (e). These characteristics are determined by the weight of one cubic meter of
dry granular particles (Vg) and the density (y), where
(1)
V
The density of the material of the particles, determined with an accuracy of 1%, was 2050 kg/m3. The density
of graphite in a component is 1650 kg/m3. These data agree well with those of [1]. The densities of the individual
particles were also determined (see Table 1), which lie within the limits of the above values of densities of the ma-
terial and component.
TABLE 1. Density and Weight of One Cubic Meter of Dry
Graphite Particles
Particle
Density.
Weight of one cubic meter of
stationary layer, kg/m3
batch 1
batch 2
size,
mm
kg/m3
before
operation
map-
after
operation
map-
after
operation
map-
paratus
paratus
paratus
> 2.88
1799
862
-
940
2.08
1930
874
920
978
1.44
1980
914
-
948
0.77
2019
943
1050
993
0.4
2046
_
1013
1044
Mixture
-
974
1100
1112
The mean (with an accuracy of ?210) results of
repeated determinations of the weight of one cubic meter
of dry granular material of a stationary layer, given in
Table 1, show that this weight of the layer increases with decrease in the particle size. This is due to the better fil-
ling of the volume by the small particles. Characteristic is the closeness of yg of a mixture of particles to yg of
dust-like particles of size 0.4 mm.
TABLE 2. Angles of External Friction and Natural Slope
of a Layer of Graphite Particles (Screening on laboratory
sieves)
Particle size,
mm
'Angle of ex-
ternal friction
of rest,
Idegrees
Coefficient of
external
friction of rest
IAngle of ex-
ternal friction
of motion,
degrees
'Coefficient of
I external fric-
tion of motion
Angle of
natural slope,
degrees
>3.5
2.96
2.24
1.70
1.32
1.10
0.975
0925
18?50'
19?30'
27?30'
23?30'
23?30'
24?
26? .
-27?
0.33
0.35
0.52
0.43
0.43
0.45
0.49
0.51
9?30'
6?26'
10?00'
8?40'
7?30'
13?20'
12?50'
12?50'
-0.167
0.113
0.176
0.152
1:132
0.237
0.228
0.228
39
35
.36
37
36
36
37
36
0.85
27?30'
0.52
16?45'
0.301
36
0.73
29?30'
0.57
19?40'
0.357
36?30'