SOVIET ATOMIC ENERGY VOL. 49, NO. 3

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• Original Classification: K
• Document Page Count: 60
• Document Creation Date: December 23, 2016
• Document Release Date: February 14, 2013
• Sequence Number: 3
• Publication Date: September 1, 1980
• Content Type: REPORT

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IJJIY VVJV'JJ I /?
Russian Original Vol. 49, No. 3, September, 1980 '
March, 1981
SATEAZ 49(3) 603-656 (1980)
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEPE4R
(ATOMNAYA ENERGIYA)
Ub
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET
ATOMIC
ENERGY
4
Soviet Atomic Energy is a translation of Atomnaya Energiya, a
publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency of the USSR (VAAP)
makes available both advance copies of the Russian journal and
original glossy photographs and artwork. This serves to decrease
the necessary time lag between publication?of the original and
publication of the translation and helps to,improve the quality
of the latter. The translation began with the first issue of the
Russian journal.
Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii
Associate Editors: N. A. Vlasov and N. N. Ponomarev-Stepnoi
Secretary: A. I. Artemov
I. N. Golovin
V. I. l l'ichev
V., E. Ivanov
V. F. Kalinin
P. L. Kirillov
Yu. I . Koryakin
A. K. Krasin
E. V. Kulov
B. N. Laskorin
V. V. Matveev
I. D. Morokhov 4
A: A. Naumov
A. S. Nikiforov
-A. S. Shtan',
B. A. Sidorenko
M. F. Troyanov
E. I. Vorob'ev'
Copyright ? 1981, Plenum Publishing Corporation. Soviet Atomic Energy partici-
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
March, 1981
Volume 49, Number 3
ARTICLES
The Energy Source of the Sun - N. A. Vlasov
. .
. . . . .
.
. . . . . .
Loop Installation with Organic Coolant for
Mir
Reactor-
- V. A. Tsykanov, P. G. Aver'yanov,
V.
P.
Anisimov,
Yu. A. Kabanov, E. P. Klochkov, V.
A.
Kuprienko, A.
S.
Kusovnikov,
September, 1980
CONTENTS
. . .
L. N. Rozhdestvenskaya, Yu. G. Simonov, and V. V. Sidorov . . . . . . .
Calculation of Hydraulic Resistance of Clusters of Rods with Heat-Exchange
Lattice-Intensifiers - V. K. Ivanov and L. L. Kobzar' . . . . . . . . .
Electron Spectroscopy of Oxidation of Steels in N204-Based Coolant
- A. G. Akimov, L. P. Kazanskii, V. S. Zotikov, P. P. Stanishevskii,
V. K. Dubinin, and V. V. Gladyshev . . . . . . . . . . . . . . . . . . .
Catalytic Fluorination of Uranium Tetrafluoride and Uranyl Fluoride
- G. A. Yagodin, ~. G. Rakov, V. I. Goncharov, S. V. Khaustov,
S. A. Sharkov, and V. A. Yurmanov . . . . . . . . . . . . . . . . . . .
Long-Term Strength of Electrical Ceramics under a Low Fluence
- Yu. B. Zverev, V. I. Ponomarev, N. S. Kostyukov,
and Yu. F. Tuturov . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mechanism of Radon Transfer in Rocks and the Depth of Emanation Methods
of Looking for Radioactive Ore - M. M. Sokolov, V. K. Titov,
V. A. Venkov, E. E. Sozanskaya, T. L. Avdeeva, and E. I. Kuvshinnikova
A Semiempirical Expression for Calculating Average Energy Losses
by Heavy Ions in Matter - E. L. Potemkin, V. V. Smirnov,
and V. V. Frolov . . . . . . . . . . . . . . . . . . . . . . . . . . .
LETTERS TO THE EDITOR
Possibility of Using Oxalic Acid Solutions for Decontaminating the Coolant
Circuit of the RBMK-1000 (Reactor) - L. A. Mamaev, V. K. Nazarov,
A. A. Malinin, V. V. Morozov, and E. I. Yulikov . . . . . . . . . . . .
First-Pass Neutrons in Equations for the Albedo of Media - S. V. Voitovetskii
and V. V. Orlov . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spectral and Angular Characteristics of the Proton Component of the Field
of Radiation beyond the Shielding of a Synchrotron at Energy 660 Mev
- V. E. Aleinikov, M. M. Komochkov, A. R. Krylov,
G. N. Timoshenko, and G. Khan . . . . . . . . . . . . . . . . . . . . .
Slow-Neutron Distribution in Polycrystalline and Single-Crystal Silicon
Samples - 0. N. Efimovich, S. P. 6olov'ev, E. S. Stariznyi,
A. A. Stuk, V. V. Sumin, and V. A. Kharchenko . . . . . . . . . . . . .
Mutual Influence of Hot-Loop Channels in Water Reflector
- N. I. Rybkin, E. S. Stariznyi, R. B. Novgorodtsev,
and V. V. Tishchenko . . . . . . . . . . . . . . . . . . . . . . . . .
Dynamics of Reactors with Positive Reactivity Feedback
- E. F. Sabaev . . . . . . . . . . . . . 0 0 0 . 0 0 0 , . . . . . . .
Engl./Russ.
603
155
0610
161
612
163
616
166
620
169
625
173
628
176
632
179
637
183
641
186
644
188
646
189
649
191
652
193
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CONTENTS
(continued)
Engl./Russ.
Cross Sections for (n, p) and (n, a) Reactions on Chromium, Iron,
Copper, and Molybdenum Nuclei at a Neutron Energy of 14.8 MeV
- 0. I. Artem'ev, I. V. Kazachevskii, V. N. Levkovskii,
V. L.. Poznyak, and V. F. Reutov . . . . . . . . . . . . . . . . . . . .
The Russian press date (podpisano k pechati) of this issue was 8/22/1980.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
A remarkable rejuvenation and birth of new ideas has been taking place in solar physics
in the last decade. The principal reason for this rejuvenation is the neutrino deficit de-
tected in the observations of Davis [1] in comparison with the predictions based on the stan-
dard models of the sun. Attempts to achieve consistency of the calculations with the ob-
servations by revision of the standard models and reevaluation of the constants used in the
calculations have not led to comforting results. The deficit has been maintained; therefore,
researchers have begun to doubt the premises on which the standard models are based. Sug-
gestions have appeared that the interior of the sun is appreciably richer in the heavy ele-
ments than the outer visible layers and that mixing of material is occurring in the solar in-
terior. The more unexpected hypotheses have been directed towards searches for unknown ef-
fects, e.g., new particles or new types of interaction (in addition to the four known), the
inclusion of the gravitational interaction of black holes, and assumptions of different neu-
trino transformations on the way from the sun to the earth. This abundance of hypotheses has
created the impression of serious trouble in solar physics. Actually, the situation is not so
alarming. It is true that some "first approximations" are in need of review, but many "luna-
tic" ideas are clearly unsound and scarcely deserving of discussion. On the other hand, ob-
servations are revealing new phenomena whose analysis promises real ways to resolve the prob-
lem.
Gravitation and Energy Sources in the Universe. The most powerful energy-generating
processes in nature occur under the action of gravitational forces. Due to its universality
and slow decline with distance, the gravitational interaction involves enormous masses of
matter. The larger the masses of the bodies are. the more significant are the gravitational
forces. We observe such effective phenomena as the burnup of meteors and the fall of meteor-
ites already on such a small celestial body as the earth (M = 6.6.1027 g). On the moon and
the planets large meteorites have formed craters and were in general one of the chief factors
determining the nature of planetary evolution. The formation of the sun and the solar system
occurred under the action of gravitational forces. It is almost indisputably recognized that
the origin of all celestial bodies, planets, stars, intragalactic star clusters, galaxies,
clusters of-galaxies, and superclusters, is due to the gravitational contraction of matter.
In the course of stellar evolution the gravitational contraction is slowed down at some stage
by transformations of matter within.the stars. But in the final evolutionary stages gravita-
tional contraction turns out to be decisive. It leads to the formation of very dense objects:
white dwarfs, neutron stars, and black holes. The formation of such objects is usually ac-
companied by large explosive processes of energy liberation - the outbursts of novae and super-
novae. Although nuclear transformations, e.g., thermonuclear carbon burning, may be the
direct cause of the explosions, gravitational contraction serves as the original energy source.
In a supernova'outburst of a star an enormous amount of energy is liberated - ti1052 ergs (1
erg = 1.10-7 J). A supernova emits more energy in a week than the sun does in its entire
lifetime of 1010 years.
Even more immense energy releases are observed in some galaxies and the quasars. An
amount of energy on the order of 1060 ergs = 106 MOC2 equivalent to the rest energy of mil-
lions of suns, emerges in the form of the kinetic energy of dispersing masses of material, in
the form of electromagnetic radiation of a broad spectral region from y quanta to radio waves,
and in the form of cosmic radiation. Thermonuclear reactions, in which tenths of a percent
of the rest energy are released, seem insufficient for such immense conflagrations. It is
necessary to "incinerate" an entire "galaxy of hydrogen" in thermonuclear reactions in. order
to cause such a conflagration. Whatever the mechanisms might be for the release of such great
energy, there can be no doubt that it occurs due to gravitational contraction (approach) of
large masses of material.
Translated from Atomnaya Energiya, Vol. 49, No. 3, pp. 155-161, September, 1980. Origi-
nal article submitted March 27,.. 1980.
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Tenths of the rest energy can be released in the process of gravitational approach. For
example, there exist states in the gravitational field of a rotating dense body to which a
transition results in the radiation of 0.4Mc2' [2]. Consequently, the energy release in the
process of gravitational contraction is more intense by one-two orders of magnitude than that
in thermonuclear fusion.
Gravitational Energy of the Sun. It is supposed that the sun was formed out of a rare-
fied cloud of gas and dust. In the process of contraction of the cloud gravitational energy
was released approximately in the amount kGMo/Ro = 5.6.1' 8 ergs (G is the gravitational con-
stant, MO and Ro are the mass and radius of the sun, and k z 1). This value depends in gen-
eral on the final state of the sun, e.g., on the radial distribution of the mass, but reason-
able variations of the distribution change the gravitational energy by less than a factor of
two. If one divides the gravitational energy of the sun by the number of nucleons in it (N =
1.2.1057), the result can be assumed to be the average binding energy of a nucleon in the sun,
which is equal to ti3.7 keV/nucleon.
The escape energy of a hydrogen atom from the surface of the sun (tit keV) exceeds by more
than two orders of magnitude the energy of the'chemical bonds of hydrogen in molecules and
condensed bodies but is ti103 times less than the energy of the nuclear bonds of a nucleon and
ti106 times less than its rest energy.
If the luminosity of the sun were. to be equal from the very start to its present lumi
nosity Lo = 3.86'1033 ergs/sec, the contraction energy of the sun would last 2.1015 sec =
5.107 years. Special calculations with analysis of the evolution of the sun in the contrac-
tion stage do not alter the order of magnitude of this quantity. But the age of terrestrial,
meteoritic, and lunar material determined by measurements of the radioactivity of uranium and
other radioactive isotopes is no less than 4.5.109 years. There is no basis for assuming the
sun to be younger than 4.5.109 years. It is clear that gravitational contraction to a reason-
able present state could not provide the luminosity of the sum for billions of years. "Un- 0
reasonable" but conceivable states would be able to provide the luminosity of the sun by vir-
tue of gravitational energy. For example, if one supposes that a compact object of the black-
hole type were formed at the center of the sun, then one can maintain the power of the sun for
billions of years due to the gradual capture by this central object of the surrounding materi-
al. During the lifetime of the sun the flow rate of capture material would amount to thou-
sandths of the solar mass, i.e., several powers of ten less than the amount of hydrogen that
would be consumed in thermonuclear reactions. The hypotheses in which the neutrino deficit
is explained by the presence of black holes are based on such notions [3]. But at the present
state of physics and astrophysics the introduction of black holes into the sun hardly seems
necessary.
Already at the beginning of the present century guesses appeared that the source of the
energy of the sun and the stars might be nuclear transformations. In the 1930s certain kinds
of the necessary nuclear transformations were found, and a solid conviction developed that
they are precisely what provides a lengthy and rather stable existence for the sun and the
other stars in the evolutionary stage known as the main sequence. The relatively large energy
release of nuclear transformations ('L10-3 Mc2),even in light of their very low probability,
proves to be sufficient for the internal heating to prevent gravitational contraction fora
long time. Gravitational contraction again comes into play and becomes the chief source of
energy of subsequent transformations in stars of large mass after significant burning of the
light nuclei. In the final stage of evolution a star may be transformed into one of three
types of celestial bodies: a white (or dark) dwarf, a neutron star, or a black hole. The
radius of the dwarf is =100 times less than that of the sun. The gravitational binding ener-
gy of a nucleon reaches 1 MeV in the dwarfs [4], i.e., less by approximately (in all only) an
order of magnitude than the nuclear bonds of the nucleons. Just as in nuclear transformations,
the binding energy is emitted in the form of quanta or particles. Upon the formation of
dwarfs the gravitational energy already makes up the dominant fraction of the overall energy
release of the: star.
The release of gravitational energy is even more significant in connection with the for-
mation of neutron stars.. The binding of nucleons in neutron stars exceeds by one-two orders
of magnitude the nuclear bonds; therefore, nuclear transformations play a secondary role in
the formation of neutron stars. Actually, endothermic fissions of the most stable iron nuclei,
which utilize part of the energy of gravitational contraction, predominate. Notwithstanding
this fact, the formation of neutron stars leads to colossal explosions of the supernova out-
burst type.
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The energy release in connection with the formation of black holes differs insignificant-
ly from the energy release in connection with the formation of neutron stars. The radius of
a solar-mass neutron star is three times larger in all than the so-called gravitational ra-
dius (Rg = 2GMo/c2 z 3 km), at which the gravitational force becomes irresistible.
The sun should be transformed into a white dwarf in several billion years. It does not
have enough mass for transformation into a neutron star or a black hole. Consequently, in the
evolution of the sun gravitational energy will add only a little bit in the late stages to
what the thermonuclear burning of hydrogen will. provide. Gravitational forces are important
for the contemporary sun only as a counteraction to the internal pressure of the hot matter
which determines its state. The equilibrium between internal pressure and gravitational con-
traction is usually disrupted in nonsteady stars, and vibrational or explosive phenomena are
observed. The gravitational forces emerge here as an active beginning which affects the na-
ture of the evolution.
We have become accustomed to considering the sun in its present state to be practically
a stable star, although flares, vortices, spots, and so on are visible on its surface. The
surface instabilities weakly affect the integrated luminosity. The so-called solar constant -
the flux of solar energy per 1 cm2 of the earth - has remained constant within 1% limits dur-
ing astronomical measurements. But the duration and accuracy of the measurements of the solar
constant are insufficient to exclude completely global irregularities. On the one hand, hy-
potheses have appeared in connection with the neutrino deficit concerning variability of the
nuclear burning processes in. the. solar interior, and on the other hand - signs of powerful
nonequilibrium processes have been detected by, the latest contemporary measurements. The pos-
sibility is not excluded that some variations of the energy release are produced by mutual
conversions of gravitational energy into thermal and vice versa. Theoretically possible meth-
ods of maintaining the energy release of the sun by virtue of gravitational contraction energy
for billions of years seem improbable. Thermonuclear burning of hydrogen and light elements
as the energy source of the sun and the stars is in such good agreement with numerous and di-
verse observations that there are no reasons to doubt it. Of course, refinements of the de-
tails of the process and variation of the steps of thermonuclear fusion are possible. But it
is unthinkable to exclude thermonuclear fusion from the energy release and evolution of the
stars.
Nuclear Transformations. Nuclear energy is released in the solar interior as a result
of the conversion of hydrogen into helium. The principal cycle of nuclear reactions is as
follows:
p + p -> d + e+ + v; d + p _ 3IIe + y;
3He + 3He _*'4 He + 2p.
Four protons are converted into an a particle. An energy of 26.7 MeV is released.. The great-
er part of this energy is imparted to charged particles and photons and then is slowly car-
ried out to the outer layers of the sun, from which it is emitted principally as visible light.
A small part (ti2%) of the energy is transported by neutrinos and carried off without hindrance
by them to the far cosmos.
The initial reaction of the cycle is the (3-decay of a pair of protons with their trans-
formation into a deuteron. The decay occurs only at the brief instants of the approach of
protons during collisions; therefore the probability of the decay is very small, and the trans-
formation of hydrogen into deuterium proceeds very slowly. The sun owes its lengthy existence
to this fact.
In addition to the hydrogen cycle of::reactions noted above, there is still the Bethe car-
bon cycle. In it four protons are also transformed into an a particle with the help of cata-
lyst nuclei of carbon and nitrogen. Also a pair of neutrinos occurs for each a particle, but
their energy is somewhat larger and the spectrum is different. The role of the carbon cycle
is small in the solar energy budget. This fact was clear already from the preliminary cal-
culations of solar models and has been confirmed by the observations of Davis.
Notwithstanding the very slow process of hydrogen burning, it releases enough energy to
maintain the luminosity of the sun. With a luminosity L - 4.1033 ergs/sec, 23.6.1038 hydro-
gen atoms per second should be converted into helium. Their mass is AM z 5.7'101`' g/sec. At
this rate ti8.1031 g 0.04Mo should be burned in 4.5.109 years. Consequently, in order to
maintain the luminosity at the present level for 4.5 years, it is sufficient to convert
a total mass of hydrogen of about 4% of the solar mass into helium.
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The observations of Davis have raised doubts about the characteristics of the nuclear re-
actions occurring in the sun. Papers (e.g., [5]) have appeared in which possible errors in
the calculations due to uncertainty of the original nuclear data are analyzed. The principal
reason for the uncertainty lies in the fact that the majority of the values of the probabili-
ties and cross sections of the reactions could not be verified directly by experiment but
were obtained by extrapolation from known analogous phenomena or from a distant energy region.
The initial reaction p+ p -> d + e+ + v has such a small cross section that there have not yet
been attempts to observe it in the laboratory. The cross section is determined on the basis
of data on pp-scattering at low energy which characterize the initial state and from an esti-
mate of the matrix element of the S transition which has been determined for. other nuclei, in
particular for a free neutron. Refinement of the data on the period of neutron decay may af-
fect the adopted value of the cross section of the reaction.
The other subsequent nuclear reactions could also not be observed directly in the labora-
tory, and their cross sections are obtained by a distant extrapolation in the energy. The
thermal energy of particles at the center of the sun is on the order of 1 keV, but the Cou-
lomb barrier for a proton is 100 keV in the best case, and the energy range accessible for
laboratory measurements starts near 1 MeV. Uncertainty in the extrapolation can have a sig-
nificant effect on the calculations for the yield of the different branches of the cascade
of nuclear reactions, in particular, on the yield of 8B nuclei, which is significant for the
neutrino measurements. In this connection., a suggestion has been made about a resonance of
the 3He + 3He reaction and the inaccuracy of the extrapolation of the cross section of the
7Be + p reaction.
An analysis of the possible changes of the adopted nuclear data has not led to agree-
ment of the standard solar model with the observations of the neutrino flux [6]. It has not
proved possible to explain the neutrino deficit by errors in the determination of the nuclear
constants.
Solar Neutrinos. The total flux of solar neutrinos 0,2 10311 v per second) is easily
estimated by knowing that a pair of neutrinos is necessary for each 26 MeV of emitted energy.
A flux of 6.5.1010 v/(cm2?sec) is incident on the surface of the earth. This number is known
rather reliably. Neutrinos carry off only a small (2-3%) fraction of the energy, and its un-
certainty is almost insignificant in the energy balance of the sun. But the nature of the
neutrino spectrum is very important for their observation. The probability of recording
neutrinos depends very strongly on their energy. The setup of Davis with a chlorine detec-
tor is practically insensitive to the neutrinos of the hydrogen cycle and has been designed
to record the neutrinos of the clearly low-probability secondary reactions.
The threshold of the 37Cl(v, e-)37Ar reaction (ti0.814 MeV) exceeds the limit of the
neutrino spectrum of the p+ p - d.+ e+ + v reaction (0.412 MeV), and the reaction 2p + e- -->
d + v, which is less probable only by afactor of several hundred, gives neutrinos with an
energy of 1.442 MeV, which exceeds the threshold of the detector. Along with the main reac-
tion 3He + 4He -} 7He + 2p, the reactions 3He + 4He -} 7Be + y and 7Be +.p --} 8B + y and the de-
cay 8B -}8Be + e+ + v are possible. An emitter of very energetic neutrinos - 8B - is found
in this chain of reactions. The limit of the spectrum of v(6B) is equal to 14 MeV, and the
average energy is 7.4 MeV.
The neutrino deficit observed by Davis refers primarily to the 6B neutrinos. Undoubt-
edly, there are fewer of them by several times than would be expected in the standard models.
The newest data are as follows: 6-7 SNU were expected [7], and 2.2 ? 0.4 SNU are observed [8].
Here a SNU is the solar neutrino unit, which is equal to 10-36 37C1 + V -} 37Ar transfcrmation
events per second on the earth.
The accumulation of observational results for 10 years has given a positive result. Al-
though there are fewer neutrinos than expected by several times, they are undoubtedly being
recorded with a noticeable excess of the effect above the background. It is true that the
accuracy of the measurements is still always low, and this is not surprising when the average
rate of formation of 37Ar in the detector does not exceed one atom every 2 days. Neverthe-
less, an attempt has been made [9] to analyze the seasonal behavior of Davis' results. It
turned out that from May to August, when the earth is farther from the sun, the number of de-
tector counts is less by. 1.1 ? 0.6 SNU than during the winter months. If this difference is
real and if the cause is the transformation of neutrinos from one kind to another (proposed
by Pontecorvo), then the difference in the neutrino masses Am2 = 4.10-10 eV2.
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200 -
780 a
~n 160
C 140
- I
-I
-1
-I
y 40 In
II\
20
0
1600 1640 1680 1720 1760 1800 1640 1880 1920
Af4C,
-20
-10
0
10
20
Fig. 1. a) Results of observations of solar activity for 400,
years and b) the 14C content in the annual rings of trees
since the year 1100 (--) and variations of the terrestrial
climate (---).
First of all, it follows from the observations that the temperature at the center of the
sun is lower than was assumed. The yield of 8B is proportional to a very high (>13) power of
the temperature, therefore, a chlorine detector is similar to a sensitive thermometer for mea-
suring the central temperature of the sun. In the first attempts to explain the neutrino de-
ficit people were seeking a way to bring the solar mode]- into agreement with a reduced cen-
tral temperature.
First of all, the opacity of the interior material was subjected to careful calculations
[10.]. The flux of energy from the center to the outer layers of the sun is transported pri-
marily by photons, which diffuse through the matter of the interior. The greater the average
mean free path of a photon is, the more rapidly the diffusion proceeds and the smaller is the
required temperature gradient. Consequently, a decrease of the opacity (an increase of the
average mean free path of a photon) leads to a flatter temperature run, i.e., a decrease in
the central temperature. The opacity depends strongly on the amount of heavy elements (heav-
ier than helium), since the absorption of photons occurs most strongly by bound electrons (the
photoelectric effect). The composition of solar matter is characterized by its content of
hydrogen (X), helium (Y), and the remaining elements (Z): X + Y + Z = 1. Spectral analysis of
the upper layers of the sun gives [11] the following values X = 0.78, Y = 0.20, and Z = 0.02.
But even at the surface of the sun Z is not determined very reliably, and.this value is taken
to lie within the limits from 0.01 to 0.04 in various model calculations. If the composition
of the material at the center differs from the surface only in the values of X and Y due to
hydrogen burning but Z is the same, the calculations of the opacity do not yield the neces-
sary reduction of central temperature. Then ideas are advanced to the effect that Z is less
at the center than at the surface and there were less heavy elements during formation of
the sun but they have then been captured at the surface from the interplanetary material or
upon passage through the interstellar medium [12].
Hypotheses. have been discussed about mixing of material inside the sun with this same
purpose. It is assumed in connection with the construction of the standard models that the
young sun was uniform in chemical composition, since it passed through a stage of strong mix-
ing by convective motions in the process of formation. Mixing in the present sun is assumed
only near the surface to a depth "0.2Ra, but all the rest of the interior preserves its ini-
tial composition, and only near the center does hydrogen burn and helium get formed. Ap-
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040003-0
v, m ?sec- 1
1,0
0,5
-0,5
0
Period 160.010 min
Fig. 2. Oscillations of the central
region of the surface of the sun from
observations (a) at Crimea in 1974-
1978 and (b) at Stanford in 1976-1978.
The period is 160.010 min.
preciable change in X (a decrease) and Y (an increase) start only at a radius 0, not isotropically but in proportion to l/(nQ) , so that the probability
of free flight of the neutrons right through the cylinder is different from ~o and is equal
to
exp [-l (1l)J dQ
(nQ)>O ~o= , dQ (6)
(n4)>0
As a result, for S,(R) we get the equation
aFl Es- N1 -2P1(2E-Es)+Es(01+kPo)2+2Eskpo
eR R
with the boundary condition (31(0) = 0.
In the many-group representation
a 1 =~s+Es~1+F'1?s+~s (1'ok)- R1 -2EiY1-
261Eh+K2.,_P1.+j~E8 (Pok)k+(Pok)i Es+(Pok)2 Es61+((iok)i Es (Pok)h;
exp [-Xil (Q)] (nQ) dQ
Poi= (nQ) > o
S (n?1l)d(2
(ng)> 0
(fSoki)- 1 - apoi + 1-poi
Ei 1 OR R
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040003-0
The equations are written in matrix form, where Rik is the probability that, after enter-
ing the cylinder with an energy of group i, a neutron will emerge from the cylinder with an
energy of group k. Let us note that (13ok) and 8oi depend only on EiR and they can thus be
tabulated and used in further calculations. For a sphere, the quantity 1/R in Eqs. (7) and
(8) is replaced by 2,R and kcyl by ksph. In the equations for plane layer we have 1/R - 0
and So = 0. Table 1 gives the results of numerical solution of Eq. (7) for a uniform cylin-
der while Tables 2. and 3 give the results of two-group calculation of nonmultiplying and mul-
tiplying uniform cylindrical slugs. In Table 3, the values in parentheses are those of the
albedo obtained by considering the given slug as a. two-layer system consisting of a slug of
radius 1.02 cm and a layer of thickness 0.18 cm. For comparison, Table 3 also gives the re-
sults of calculations by the Monte Carlo method. We studied the solutions of the equation
for the albedo of the medium outside the cylinder and the sphere:
aR 4p-H(1-lf C1-P)
With the condition that 8R. = R_ the albedo of the half-space and H = Es/E, a is
equal to 0 for the plane case, 1 for the cylindrical case, and 2 for the spherical case. In
the limit for nonabsorbing media (H = 1) Eq. (10) has one solution 8cyl = 1 for the cylinder,
and two solutions Rsphi = 1 and Rsph2 = R/(l + R) for the sphere. The appearance of two solu-
tions in.the latter case can be understood. by, considering a finite spherical nonabsorbing
layer A. If the condition of total reflection exists on its outer surface, then S = 1 and
remains the same as A --> -. If total reflection does not occur on the outer surface, then.
part of the neutrons move off to infinity and S(R) < 1. In the cylindrical (as well as in
the plane) case the neutron current through a cylindrical surface with a large radius p tends
to 0 as p -} - so that the boundary conditions at the remote surface do not affect the albedo
and B = 1. The validity of these assertions is easily verified by solving the respective
equations in the diffusion approximation. We carried out calculations of Eq. (10) for H j 1.
It was expected that the absence of unscattered neutrons in the reflected flux in this case
ensures adequate accuracy of Eq. (10). Comparison with the results of [5] for R = 1 and H =
0.8, however, revealed substantial discrepancies which require further analysis.
LITERATURE CITED
1. V. V. Orlov, At. Energ., 38, No. 1, 39 (1975).
2. V. V., Orlov and V. S. Shulepin, At. Energ., 41, No. 6, 434 (1976).
3. G. Stuart, Vopr. Yad. Energ., No. 6, 71 (1958).
4. V. A. Ambartsumyan, Theoretical Astrophysics [in Russian], Gostekhizdat, Moscow (1953).
5. A. Kavenoky, Nucl. Sci. Eng., 65, 209 (1978).
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040003-0
SPECTRAL AND ANGULAR CHARACTERISTICS OF THE PROTON COMPONENT OF THE FIELD
OF RADIATION BEYOND THE SHIELDING OF A SYNCHROTRON AT ENERGY 660 MeV
V. E. Aleinikov, M. M. Komochkov, A. R. Krylov, UDC 539.125.4.:164
G. N. Timoshenko, and G. Khan
Reference [1] studied the angular distribution of the flux of protons beyond the con-
crete shielding of the supercyclotron laboratory of nuclear studies at the JINR. The next
step in studying the proton component of the radiation field beyond the shielding of this
accelerator is to measure the spectral and angular distribution of protons with energy great-
er than 40 MeV, which we have carried out for two variants of the experimental geometry.
The goal of this work, as in [1], is to obtain the primary experimental data for check-
ing the methods of calculating various parameters of the radiation field beyond the shield-
ing of an accelerator.
In the first variant of the experimental geometry (Fig. 1), a collimated beam of 630-MeV
protons impinged on a concrete shield of thickness 2 m (470 g/cm2) at an angle of 30?. In
the second variant, the primary beam of protons was fully stopped in a copper target with a
diameter of 12 cm and a thickness of 30 cm, placed 4.8 m from the target in the direction of
i
00
/ 1 \\
9-17? I 0? \\ 10?
Fig. 1. Geometry of the measurements.
0 I __ luigwiiillil
l~lll
20 60 100 140 180 220 260 E, Me V
Fig. 2. Proton spectra at point 2, mea-
sured in the first variant of the experi-
mental geometry.
Illldl
-1d 'I,
hi
141/1
111
111111III114
ryl pl4Wi'm . 2
p.lu.....
Fig. 3. Proton spectra at points 1 and 3,
measured in the first variant of the ex-
perimental geometry: 1) point 3, P = 0?;
2) point 1, q)= 30?.
Translated from Atomnaya Energiya, Vol. 49, No. 3, pp. 188-189, September,` 1980. Origi-
nal article submitted September 28, 1979.
644 0038-531X/80/4903- 0644$07.50 ? 1981 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040003-0
70 Illllllllpllvq lh
hgplllh 4111111
'II
Fig. 4. Proton spectra at point 2, mea-
sured in the second variant of the ex-
perimental geometry.
41,1 =-JO?
III
~
60 700 9110 760
the beam, which served practically as a plane monodirectional source of the radiation inci-
dent on the shield [2]. The proton spectra were measured by a AE spectrometer. The pro-
tons exited the shield at points 1, 2, and 3 at various angles ;0 to the normal in the hori-
zontalplane. The physical angle and angular acceptance of the spectrometer for measurements
in the first and second variants were, respectively, 19.5.10-3 sr, 4.5?, and 33.3'10-3 sr,
12.1?. The initial construction of the spectrometer and the method of reconstruction of the
proton spectra from the experimental data were described in [3,.4]. The evaluation of the
fractions of electron and Tr-meson components of the total charged particle flux was accom-
plished as in [1]. To determine the error in the measurements, the statistical error in the
analyzer channels and the apparatus error were calculated. Figure 2 shows the dependence of
the proton spectra measured in the first variant of the geometry at point 2 at anglecp. The
ordinate is the differential angle and energy proton flux, F(r, Sd, E), for energies from
Emin and Emax at point r on the surface of the shield, multiplied by coscpand normalized per
primary proton [1]. Here S2 is the direction of motion of the proton detected by the spec-
trometer. The hardest of the spectra shown is that measured at 'P= 17?, at the maximum of
the angular distribution of the proton flux at the given point. The proton spectra at points
1 and 3, measured, respectively, at i = 30 and 0? in the first variant of the experimental
geometry,are shown. in Fig. 3. The spectrum at point 1, measured in the direction of the
incident protons, is the hardest of all those obtained. On the other hand, the spectrum at
point 3 is essentially softer than that at point 2, measured at q)= 0. Figure 4 shows the
proton spectra measured at point 2 in the second variant of the experimental geometry.
In conclusion, we note that to analyze the systematics of the radiation spectra beyond
the shielding of accelerators, it is necessary to further accumulate data for various experi-
mental geometries and various sources of primary radiation, particularly for a higher energy
of the accelerated protons.
The authors wish to thank A. N. Resunik and V. A. Kulikov for help in carrying out
these experiments.
1.
V.
E.
Aleinikov et
al. ,
JINR Preprint
P16-11891,
Dubna
(1978).
2.
V.
E.
Aleinikov et
al.,
JINR Preprint
P16-8179,
Dubna
(1974).
3.
V.
E.
Aleinikov et
al.,
JINR Preprint
P16-94006,
Dubna
(1975).
4.
G.
N.
Timoshenko et
al.,
Kernenergie,
21, 181 (1978).
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040003-0
0. N. Efimovich, S. P.. Solov'ev, E. S. Stariznyi, UDC 621.315.592
A. A. Stuk, V. V. Sumin, and V. A. Kharchenko
At present the method of nuclear transmutations [1] is being more and more widely used
to produce semiconductor silicon. This method permits quite accurate control of the phos-
phorus impurity introduced in the reaction 30Si(n,,y)31Si - 31P. The material obtained in
this way is much more uniform than that produced by conventional doping methods [2]. This
is very important in the manufacture of semiconductor devices.
With increasing size of the crystals being doped the uniformity of the distribution of
the impurity introduced is decreased as a result of the self-shielding of the neutron flux
by the sample. Therefore, in the practical application of the nuclear transmutations method
it is necessary to know and to take account of the slow-neutron flux density distribution in
the silicon samples. This problem is becoming very urgent in view of the trend toward the
use of larger and larger silicon single crystals in the manufacture of semiconductor devices.
The slow-neutron flux density distribution in a sample can be determined by knowing the
total interaction cross section and its components - the absorption and scattering cross sec-
tions. For materials in which the scattering cross section is larger than the absorption
cross section the analysis of the distribution also necessitates taking account of the state
of the crystal structure and the temperature of the bombarded sample. However, there are
practically no such data in the literature for silicon single crystals.
In the present article we present measured values of the total interaction cross section
of neutrons with silicon nuclei as a function of the neutron energy and the temperature and
crystal structure of the sample. The attenuation of the neutron flux in silicon samples of
various sizes was investigated also.
The experimental arrangement was described in [3]. The. intensities of the slow-neutron
beam incident upon and transmitted through the sample were measured as functions of energy.
The interaction cross section was found from the relation
I/Ia = exp (-Nax), (1)
where Io and I are, respectively, the intensities of the incident and transmitted neutron
beams; N,..number of silicon nuclei per unit volume; a, interaction cross section; and x,
length of the sample.
In the neutron energy range investigated the change-in flux density in the polycrystal-
line samples is independent of energy, as might be expected. In the single-crystal samples
the attenuation depends on the neutron energy. The attenuation the maximum at n0.4 eV and
TABLE 1. Nuclear-Physical Characteris-.
tics of Polycrystalline and Single-Crys-
tal Silicon
Neu-
tron
Single-crystal silicon,
T = 300?K
Polycrystalline sili-
con. T = 300?C
energy,
eV
at, b
aa, b
as, b
q'tr'
I
Qt'
q'tr'
cm
b
cm
0,4
1,68?0,08
0,04
1,64?0,08
11,9
0,054
0,54?0,02
0,11
0,43?0,02
37,0
12
25
11
0,0256
0,42?0,02
0,16
0,26?0,02
47,6
,
0,016
0,40?0,02
0,20
0,20?0,02
47,7
Translated from Atomnaya Energiya, Vol. 49, No. 3, pp. 189-191, September, 1980. Origi-
nal article submitted November 12, 1979; revision submitted February 18, 1980.
? 1981 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040003-0
Fig. 1 Fig. 2
Fig. 1. Energy dependence of total cross section in polycrystalline and single-
crystal silicon samples at temperatures of 700 (A), 500 (c), 300 (A), and 80?K (1Q;
U) experimental data for polycrystalline silicon; ?) data from [4]; 1, 2) calcu-
lated in [8] for single-crystal samples; 3) as as a function of neutron energy [8].
The dimensions of the symbols correspond to the statistical errors of the measure-
ments.
Fig. 2. Relative radial neutron flux density distribution in (1) polycrystalline
and (2) single-crystal silicon samples; ?) experiment; ----) calculation.
above, and decreases markedly with decreasing neutron energy.
It should be noted that the attenuation of the neutron flux in our experiment was deter-
mined mainly by scattering processes, in the first place because as 0.4 eV at is the same as for a polycrystal. With a de-
crease in neutron energy at decreases from 2 to 0.45 b (1 b = 10-2B m2). The calculated
values of at, as, and as for polycrystalline and single-crystal silicon are summarized in
Table 1. In the calculations it was assumed that as varies with neutron energy as E-11i2. The
absolute value of as was taken equal to 0.16 b at E = 0.025 eV [8].
The difference in the energy dependence of at in polycrystals and single crystals re-
sults from the difference in scattering processes. Taking account of coherent and incoherent
elastic scattering and the fact that as >> as in silicon suggests that in a polycrystal ef-
fects due to neutron diffraction predominate in the energy range investigated.' This assump-
tion is rather well confirmed by the energy dependence of at.
In a single crystal, on the other hand, the neutron flux is attenuated mainly as a re-
sult of inelastic scattering. Elastic coherent scattering makes only a small contribution
to the total attenuation, since in oriented single crystals in the geometry of the present
experiment the conditions for Bragg reflection are satisfied for only specific groups of neu-
trons. The values of the diffusion length for a polycrystal calculated from the tabulated
data are in satisfactory agreement with published data (L = 22 cm [4]), but differ apprecia-..
bly from our value L = 44 cm for a single crystal.
The calculated values of L were used to find the slow-neutron flux density distribution
in cylindrical samples along the z axis, which coincides with the direction of the generators
of the cylindrical sample, and along the radius of a two-region cylindrical cell composed of
the silicon sample and water. In the first case the calculation was perfcrmed by the formula
[5]
~P l~, Z)= 2cpo sh [Yn (H-z)]
7nJi(in) sh('' H) ' (2)
n=1
where Yn = (jn/R)2 + l/L2, J1, first-order Bessel function of the first kind; jn, n-th root
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of the zero-order Bessel function of the first kind yo, slow-neutron flux level at the end
of the sample; H and R, extrapolated length and radius of the sample [5]; and L, slow-neutron
diffusion length. The calculated values of the attenuation of the flux density in polycrystal-
line and single-crystal samples are in satisfactory agreement with the measured attenuation
of the neutron flux as a function of the length of the samples-investigated.
The radial distribution of the flux density can be found in the P1-approximation from
the relation [6]
Al, (r ) Ec+ Ss
(P V) L
(0) AEv, -- '
where A is a coefficient determined from the boundary conditions; Ec, macroscopic cross sec-
tion for the capture of thermal neutrons by the material of the sample; EEs, slowing down
power of the sample material; and Io, zero-order Bessel function of imaginary argument.
Equation (3) can be considerably simplified. To do this we expand the function Io(r/L)
in a series and retain only the first two terms, since r/L To.
Let n(T) and p(T) be some positive nondecreasing functions, let dn/dT =.p(T), and let A
be a Hurwitz matrix. Then, for any n >, n(T) and all T > To inequalities
x+> (PI-A)-1a+n(T),
x->-a-T
are satisfied only if they are satisfied at the initial moment T = To. Indeed, suppose that
x+ (pI - A)-la-Fn(T) + z. Then
dz Az dp n-n (ti) Az
T = n (PI - A)-2 a+n (i) dti (PI - A) 1 (- Aa+) n n +Q+
where z(t(,)E K. Since (A - pI) is a Hurwitz matrix, (PI -A)-' is a positive operator and,
moreover, In - n (T)]ln. _> 0, dp/di > 0, a+ C K, -Aa+ C K, whereby Q E K . This and. the positiveness of the
displacement operator with respect to the trajectories imply that zE K, i.e., that the first
inequality (for x+) holds. The second inequality is proved in similar fashion.
It follows from the definition of the cone C that bTx > 0 on C and the inequalities
proved above for x+ and x lead to the estimate
bTx > bT (pI - A)-1 a+n (t) - bTa-ti. (4)
Inequality (4) can be used to estimate ni. In this case RN = R1, a+ = A1, a = 0, A = -Xi,
and b = Ri and, therefore,
~tni > p+%. n(T), i=1, 2, ... 6.
e
Let us point out that the substitution ni = p i7j (n + zi) was used earlier (see [3, 4]) in solv-
ing the problem of bringing a reactor up to power from the subcritical state. Thus, inequal-
ity (4) can be considered as a generalization of estimates of the type of Eq. (5).
The estimates obtained make it possible to go over from the initial equations to differ-
ential inequa
6
lP+ ~](3i p+~i > 5k0 (a)+bT (PI-A)-1 a+n-bTa T;
do/dti=p; da/dT=(V/n) sign (n-1).
For n > 1, upon removing the inequality sign in Eq. (6) we arrive at a system of comparison
in R2 with a displacement operator along the trajectories which is monotonic over the cone
[0, co) x (-co, 0]. Any solution of these equations which satisfies the conditions p > 0, `
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040003-0
dp/dT > 0, and n(T) > 1, yields the sought estimate of the solutions of the initial system.
Estimates of the other variables are constructed with the aid of inequalities obtained in
deriving Eqs. (6).
Let bTa > bTa and let s be some positive number satisfying the condition s > s*; then
bT x (pI - A)-la'+s* = bTa. Assuming that n = sT and bearing in mind that 6ko(a) >dko, we
can easily ascertain that the p > s estimate is valid for all T greater than some To. With
this estimate we find that the solutions of the comparison system and, therefore, of the
initial system satisfy the inequality n > sT for T > To. Since dT/dt = n, we have T ? To
exp st and, therefore, n> sr0 exp st.
Thus, for bTa > bTa system (1) has solutions which go into infinity with an exponen-
tial growth factor greater than that preassigned. Such solutions lie in the region p > s*,
where 1/p is the reactor period.
We investigate to see whether or not this contains a set of solutions of the explosive
type. First of all, let us note that if the estimate n> (T/T)1+Y, T > 0, y > 0, is valid,
then all trajectories satisfying this estimate are of the explosive type. Indeed, from the
inequality
dtldt > (t/T)1+V t (0) = to
it follows that tV > to/ [1 - y T (T )vJ . The estimate means that n goes to infinity in a finite
time.
Thus, it is necessary to verify the inequality pT >, (1 + y)(T/T)yfor all T > To; here,
y and To are numbers which we can choose as we see fit and n = (T/T)1+y?
Using the first equation of the comparison system, we reach the conclusion that if
ak [ 1 T (T )v ( T )v v(t'lT)~ (7)
o+ bT I-A a+ -bTa-T -(1--T) } ~i (t/T) +~iT/(1~ y)
i=1
for all T >'To, then pT > (1 + y)(T/T)Y. Since bTa+ >bTa-, inequality (7) will be satisfied
if we put the constraint 0 < y < 1 and bTa:+ > bTa-(l + y) on the choice of y... Clearly, these
inequalities can be satisfied by. the choice of yl and To.
Example. Let us consider a reactor in respect of self-regulation, characterized by the
following parameters; N = 2; ao > r; b2 > b1
A II 00-r a+-11 II' a-11011 ' b=11b111
%ob1 > b2r.
The comparison equations for such a reactor are of the form
fi
"-b1 P'04 n-b2rt;
lP-f ~F1 P
+ Xi
i=1
In the given case s? = %o/(b62r(, - 1) . The comparison system is conveniently studied over the
phase plane (p, n). To this end it is necessary to eliminate the variable T. Differentiat-
ing the first equation with respect to n, we have
-}- b~0 1 dp b1.0 b2r
(P+Xi)2 1 (P+?o)2 n J do P+,%o p*
From this system we establish that the half space p > s* is filled with trajectories of the
explosive,, type. Indeed, for p > s* the variable p grows markedly with n and for large n and
p the estimates Tp > nY with y > 0 is valid.
In the general case, including when allowance is made for the control and safety system
of the reactor, the arrangement of the trajectories of they explosive type can be studied in
greater detail by computer from the comparison equation.
Conclusions. The condition.bTat > bTaj means that the reactivity feedback transfer coef-
ficient K(p).= b(?pI -.A)-la is positive for sufficiently large positive real. values of the
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040003-0
parameter p; such reactors can be called reactors with'a predominant positive reactivity feed-
back at high frequencies. An important feature of the dynamics of such reactors is the exis-
tence of a system of trajectories. of the explosive type in phase space.
1.
M. A. Krasnosel'skii,
Moscow (1962).
Positive Solutions of Operator Equations [in Russian], Fizmatgiz,
2.
M.
G. Krein and M. A. Rutman, Usp. Mat. Nauk, 3, No. 1(23), 4 (1948).
3.
D.
L. Hetrick, Dynamics of Nuclear Reactors, Univ. of Chicago Press (1971).
4.
H.
Hurwitz, Nucleonics, 5(1),: 61 (1949).
5.
S.
A. Chaplygin, Collected Works [in Russian], Vol. 1, Ob'ed. Gos. Izd., Moscow (1948):
6.
N.
V. Azbel.ov, Dokl. Akad. Nauk SSSR, 89,'No. 4, 589 (1956).
7.
M.
A. Krasnosel'skii, Operator of Translation along Trajectories of Differential Equa-
tions, Amer. Math. Soc. (1968).
CROSS SECTIONS FOR (n, p) AND (n, a) REACTIONS ON CHROMIUM, IRON,
COPPER, AND MOLYBDENUM NUCLEI AT A NEUTRON ENERGY OF 14.8 MeV
0. I. Artem'ev, I. V. Kazachevskii, V. N. Levkovskii, UDC 539.172.4
V. L. Poznyak, and V. F. Reutov
The cross sections for (n, p) and (n, a) reactions on Cr, Fe, Cu, and Mo nuclei have
been measured in many works. The published data, however, are still incomplete and contra-
dictory [1, 2]. Insofar as these elements enter into the composition of the proposed con-
struction materials of a thermonuclear reactcrs, it would be useful to measure the cross
sections of these reactions.
This work measured the cross sections for (n, p) and (n, a) reactions by an activation
method using a semiconductor y spectrometer. The cross sections were determined by comparing
the intensity of the characteristic y lines produced by the studied and standard reactions.
TABLE 1. Cross Sections for the (n, p)
and (n, a) Reaction, mb*
Reactions
This
work Data [1, 2]
52Cr (n, p)62V
84?8
118116; 105?10; 90?10;
83?6; 78?11; 74?10; 73?5
53Cr (n, p)53V
47?6
44?5; 44?7; 36?6
54Cr (n, 1))54V
15?2
16?3; 15?2; 13,5?1,5
54Cr (n, a)51Ti
9?2
12,5?1,3; 8?0.8; 7?1
54Fe (n, p)54Mn
310?30
382?13; 368?28; 333?67;
310?25; 300?20; 259?26;
254?23
54Fe (n, a)51Cr
90?15
131?34; 109?10; 92?37;
90?10
93Cu (n, a)80Co
41?8
36?2,5; 34?2,4; 34?4
65Cu (n, a)62Co
5,7?0,6
14?10; 7,5?2
95Cu (n, a)12MCo
8,0?1,6
1,9?0,6
92Mo (n, p)02mNb
53?5
62?4; 60?15; 14,5
92Mo(n, a)89Zr
19?2
25?15; 20?8; 19?1,5
95Mo (n, p)9$Nb
40?5
-
95Mo (n, p)95mNb
7?2
-
95Mo (n, p)98Nb
22?2
37?9; 21?7; 21?1,5; 16?3
97Mo (n, p)97Nb
17?2
110?20; 108?54; 68?14;
17,1?1,5; 15,9?1,3
97Mo (n, p)97mNb
7,0?0,7
7,4?0,8
98Mo (n, p)98Nb
9?1
19?3; 9?2; 6,7?0,5;
4,1?0,5
99Mo (n, a)95Zr
5?1
8,1=0,0
'??Mo (n, a)97Zr
2,5?0,3
14?6
Translated from Atomnaya Energiya, Vol. 49, No. 3, p. 195, September, 1980. Original
article submitted December 17, 1979.
0038-531X/80/4903-0655$07.50 ? 1981 Plenum Publishing Corporation
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Copper (reactions 65Cu(n, 2n)64Cu) and aluminum (reactions 27A1(n, a)24Na) foils were used
as standards. Irradiation was conducted on the neutron generator at the Institute of Nuclear
Physics of the Academy of Science Kazakstan,. USSR [3]. Isotopically enriched targets were
used to measure the cross sections of Cr and Mo. The determination of the cross sections of
the Mo isotopes was complicated by a large y background from the matrix and the presence of
y lines of similar energy (e.g., 99Mo and 97Zr have, respectively, 739 and 743 keV; 95Zr and
95Nb have 758 and 764 keV, respectively), in-connection with this the products of the (n, p)
and (n, a) reactions on Mo were chemically separated from the target by a somewhat modified
method which is described in [4].
The measurements of the cross sections of the reactions (n, p) on Cr, Fe, and Mo, in
the majority of cases, satisfactorily agreed with the mean values of the published data (see
Table 1). The measurements of the cross sections for the (n, a) reaction on 65Cu, 98Mo, and
i??Mo do not confirm the well-known values. The cross sections of the reactions on 95Mo were
measured for the first time in this work.
1. N. Bormann, H. Neuert, and W. Scobel, in: Handbook on Nuclear Activation Cross Sections
(1974), p. 87.
2. P. Cuzzocrea, E. Perillo, and S. Nottarigo, Nuovo Cimento, 4A, 251 (1971).
3. V. V. Sokol'skii, Thesis of the Reports of the Second All-Union Conference on Activation
Analysis-[in Russian], Tashkent (1968), p. 25.
4. D. Hume, Radiochemical Studies: The Fission Products, Paper 245, New York (1951), p.
1499.
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