THE SOVIET JOURNAL OF ATOMIC ENERGY VOL. 4 NO. 5

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• Publication Date: May 1, 1958
• Content Type: REPORT

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THE SOVIET JOURNAL OF
vol. 4, no.
May 1958
OMIC ENERGY
ATOMHa.51
3Heprllm
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, INC.
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recent Russian research
?in complete English translation
A New Method
- in the Theory of
SUPERCONDUCTIVITY
BY N. N. BOGOLIUBOV
V. V. TOLMACHEV
' AND D. V. SHIRKOV
T N THIS unprecedented complete solution
to the perplexing problem of con-
structing a microscopic theory of super-
conductivity,' the authors explain their
new .method?a result of the research of
N. N. Bogoliubov and V. 5V. Tolmachev?
baaed on a physical and mathematical
analogy with superfluidity.
Here they give calcUlations for the en-
ergy of the superconducting ground
state using Frohlich's Hamiltonian, as
--well as of the one-fermion and collec-
tive elementary excited states; they
provide a detailed analysis of the role
of the Coulomb interaction between
the electrons in the :theory 'of supercon-
ductivity; and demonstrate how a sys-
tem of ferm ions is treated with a
fourth-order interaction Hamiltonian
and establish the criterion for its ,su-
perconductivity ? all of Which is indi-
cated in greater detail in the Complete
table of contents shown to the right.
cloth bound ? 130 pages ? $5.75
Complete Table of Contents
INTRODUCTION
outline of the present state of superconductivity
theory ? brief description Of the microscopic
theory of superconductivity
FRoHLICIeS MODEL OF
SUPERCONDUCTIVITY
principle of compensation of "dangerous" dia-
grams ? analysis of the compensation equation
? the ground state and the one-ferntion excited
states
RENORMALIZED THEORY OF
SUPERCONDUCTIVITY IN
. FRoHLICH'S MODEL
compensation and renormalization equations ?
simplification of the relations obtained ? energy
difference between normal and superconduct-
ing states ? the property of superconductivity
'SPECTRUM OF
COLLECTIVE EXCITATIONS IN
THE SUPERCONDUCTING STATE
the method of .approximate second quantization
as applied to a system with Coulomb interaction
? collective excitations in Frohlich's model ?
solution of the_secular equations?longitudinal
excitations ? solution of the secular equations?
transverse excitations
INCLUSION OF THE COULOMB
INTERACTION BETWEEN ELECTRONS
statement of the Problem ? compensation and
renormalization conditions ? transition to the
lime-dependent" formalism ? final form of the
compensation equation for the electron dia-
grams ? energies of the ground state of the
one-fenttion excited state ? transformation of
the Q (1c. k') kernel ? finding X. p. and (.7)_? a
related model
QUALITATIVE DESCRIPTION OF
Errzers DUE TO
THE COULOMB INTERACTION
approximate determination of the renormalised
Wand g ? the properties of Q, and Coph ? gen-
eral properties of the basic compensation
equation
FERMI SYSTEMS WITH
AX INTERACTION
formulation of the BCS theory ? compensation
equations ? collective excitations ? influence
of the Coulomb interaction
CONCLUSION -
the thermodynamics and electrodynamics of
the superconducting state ? a qualitative pic-
ture of the phenomenon of superconductivity
APPENDICES
_ -on the question of .superfluidity in nuclear mat-
ter ? on a variational principle in the many-
- body problem
_
" CB translations by bilingual scientists in. -
dude all diagrammatic, photographic and _
tabular 'material integral with the text.
CONSULTANTS BUREAU, INC.
227, WEST 17TH STREET, NEW YORK 11, N. Y.
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vol. 4, no. 5
May 1958
THE SOVIET JOURNAL OF
ATOMIC ENERGY
ATOMNAIA ENERGIIA
A publication of the Academy- of Sciences of the USSR
Annual Subscription $75.00
Single Issue 20.00
Year and issue of first translation:
volume I, number 1 January 1956
TRANSLATED FROM RUSSIAN
Copyright 1959
CONSULTANTS BUREAU, INC.
227 W. 17th St., NEW YORK 11, N. Y.
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EDITORIAL BOARD
OF
ATOMNAIA ENERGIIA
A. I. Alikhanov, A. A. Bochvar, V. S. Emerianov, V. S. Fursov,
V. F. Kalinin, G. V. Kurdiumov, A. V. Lebedinskii, LI. Novikov
(Editor-in-Chief),V.V.Semenov (Executive Secretary).V.LVeksler,
A. P. Vinogradov, N. A. Vlasov ( Assistant Editor-in-Chief).
Printed in the United Staten
,Note: The sale of photostatic copies of any portion of
this copyright translation is expressly prohibited by the
copyright owners. A complete copy of any article in the
issue may be purchased from the publisher for $ 12.50.
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SOVIET JOURNAL OF ATOMIC ENERGY
Volume 4, Number 5 May 1958
CONTENTS
PAGE
RUSS.
PAGE
The Isotopic Constitution of Terrestrial Rocks and Meteorites. A. P. Vinogradov
541
409
Address Given in Paris, September 12, 1957. The Future of Atomic Energy. Sir John
Cockcroft
549
417
Heat Transfer in Liquid Metals. S. S. Kutateladze, V. M. Borishanskii and I. I. Novikov .
555
422
Evaluating the Economic Feasibility of Using Special Heavy Concretes for Radiation Shield-
ing. A. N. Komarovskii
573
437
Deformation Systems of a-Zirconium. Iu. N Sokurskii and L. N. Protsenko
579
443
Choice of Basic Parameters for High-Energy Linear Electron Accelerators. G. A. Zeitlenok,
V. V. Rumiantsev, V. L. Smirnov, L. P. Fumin, V. K. Khokhlov, I. A. Grishaev and
P. M. Zeidlits
583
448
Secondary Nuclear Reactions in the Bombardment of Tin by Fast Protons. M. Ia. Kuzuet-
591
455
soya, V. N. Mekhedov and V. A. Khalkin
Dose Characteristics?of a Mixture of Uranium Fission Fragments. K. K. Aglintsev, A. N.
Gorobets, V. P. Kasatkin and E. S. Kondakova
597
461
Letters to the Editor
Bremsstrahlung in Nuclear Fission. A. I. Alekseev
601
465
New Photomultipliers for Scintillation Counters. A. G. Berkovskii
604
466
Methods of Fabricating Stable a-, i3-, and y-Sources Using Inorganic Enamels. D. M.
Ziv, G. S. Siuitsyna, I. A. Efros and E. A. Volkova
607
469
Radiation Field of a Rectangular Parallelepiped with Self-Absorption Taken into Account.
L. N Posik
609
470
Activation of Air by Radiation from the Synchrocyclotron. M. M. Komochkov and V. N.
Mekhedov
612
471
Determination of Density of Ice and Snow in Antartica by Means of Gamma Rays. 0. K.
Vladimirov and V. A. Chernigov
616
474
A Radiometric Method of Control of Consecutive Transmission of Different Petroleum
Products Through the Same Pipe Line. B. Z. Votlokhin, A. Z. Dorogochinskii and
N. P. Mel'nikova
618
475
Scientific and Technical News.
The 600-Mev Synchrotron at CERN (621). Storage of Radiation Energy in Graphite
(624). On the Behavior of Plutonium Alloys (627). Some Problems of the Extraction of
Uranium from Ores (631). The Largest Operation for Mining and Processing Uranium Ores
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CONTENTS (continued?
RUSS.
PAGE PAGE
in Noncommunist Countries (635). The "Pronto Reaction of P. Ramdohr (638). Uranium
Resources in Capitalist Countries (640). A Conference on the Application of Radioactive
Isotopes in Analytical Chemistry (646). News Roundup (649).
Bibliography
Useful Translation Collection (651). New Literature (653).
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THE ISOTOPIC CONSTITUTION OF TERRESTRIAL ROCKS AND METEORITES?
A. P. Vinogradov
The lecture cites numerous data on the isotopic constitution of sulfur,
oxygen, carbon and light gases in iron, stone iron and stone meteorites. A
comparison is made between the isotopic consitution of these elements in
meteorites and in different rocks of the earth's crust. An analysis of these
data leads the author to a number of important conclusions in the realms of
geochemistry and cosmochemistry. Considering that the fractionation of
isotopes in the earth's crust is the result of differentiation of terrestrial mat-
ter, the author concludes that no such differentiation occurred in the meteor-
itic material (in which no fractioning of isotopes is observed) and that, there-
fore, all meteorites must have formed by accretion of particles of primordial
cosmic dust.
The overwhelming majority of elements are mechanical mixtures of isotopes. We know that the same ele-
ments and the same isotopes exist throughout the cosmos. On the basis of certain theoretical considerations and
empirical data on the composition of the earth, meteorites and stars, it was possible to plot a curve which shows
with some degree of probability the relation between the abundance of the nuclides in the cosmos and their mass
numbers. This curve shows an overwhelming predominance of light elements, light nuclides, in the cosmos. Al-
though our knowledge of the composition of cosmic bodies is far from perfect, we must take into account today
the undoubted differences in the distribution of elements even within the boundaries of our solar system. We can
speak even more definitely 7f the differences in the proportions of the isotopes of light elements in the planets
and in the stars. The discovery of the so-called carbon-nitrogen and proton-proton cycles not only explained the
possibility of variation in the isotopic constitution of hydrogen, carbon, nitrogen, oxygen and other light elements
in some stars, but initiated further research in that direction. This research, as you know, has led to the discovery
of isotope exchange in hydrogen, carbon, oxygen and other light elements in different types of stars.
Evidently we are not far from the truth when we insist that a continuous evolution is taking place in the
nuclide composition of the cosmic bodies of our galaxy.
The variations in the isotope ratios in different stars are the result of thermonuclear processes, of astral
nucleogenesis. But, the question arises, are these "hot* processes the only ones responsible for all of the possible
variations in the isotope ratios which we observe tit the cosmic bodies?
It is to this question that I want to draw your attention now.
The isotopic variations going on in the cold cosmic bodies are extremely small in their productivity and
final effect as compared to nucleogenesis in the stars. Perhaps there would be no need to mention them at all
if even the smallest variations in the isotopic constitution of igneous rocks or meteorites, for example, did not
to some extent point to definite processes which have led to the formation of the earth's crust and its rocks and to
the formation of different meteorite types. It is for this reason that I decided to present to you some of the results
? Lecture delivered in September of 1957 in Paris at the International Conference on the Use of Radioactive
Isotopes in Scientific Research.
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of comparative study of the isotopic constitution of the only cosmic materials which can be studied directly at
present, namely, the more deep-seated rocks of the earth, and meteorites.
Before doing this, I must remind you briefly of the nature of the earth's crust and of the different meteorite
types.
The earth is composed of a number of concentric shells: atmosphere, hydrosphere, biosphere, lithosphere
and mantle.
The earth's crust or lithosphere is the solid outer shell consisting of granitic and basaltic layers. The basal-
tic layer envelopes the entire earth. The granitic layer covers only about one-half of it. It is absent from the
bottom of the Pacific Ocean and, apparently, from the deeper basins of the other oceans. The thickness of the
basaltic layer averages 15-25 km, but is much less under the oceans. The granitic layer reaches its maximum
thickness of 15 to 20 km on the continents. The earth's crust is distinguishable in the structure of the earth not
only by its chemical composition but also by its seismic properties. At a depth of 40 km, it is separated from
the underlying materials of the mantle by the so-called Mohorovicic discontinuity. The rocks of the mantle,
such as dunite, for example, approach olivine in composition, and sometimes reach the 'earth's surface by filling
the deeper fractures in the crust. On the surfdce the earth is covered by a veneer of sedimentary rocks.
It is very probable that the igneous rocks of the earth's crust were formed during geologic time as the re-
sult of fusion \of the materials of the mantle. In order to produce high concentrations of certain elements in the
igneous rocks of the crust, for example in granites, a great thickness of the mantle material must have been
mobilized. The composition of the mantle, as accepted by most scientists with but a few minor reservations, is
identical with that of the stone meteorites known as chondrites. The identity in composition of the iron meteor-
ites and the earth's core, and of chondrites and the ultrabasic rocks of the deeper parts of its mantle was first
pointed out by G. A. Daubr6e, member of the French Academy of Science and corresponding member of the
Russian Academy of Science.
A few words about meteorites.
All meteorites belong to three main classes: a) stones, b) iron-stones and c) irons. The so-called chon-
drites predominate among the stones. Chemically they are very near the terrestrial ultrabasic rocks. The most
interesting characteristic which distinguishes them from terrestrial rocks is their structure. They are composed
of the so-called chondrules ? solidified droplets of silicate material (Figs. 1 and 2).
The chondrules are cemented together by fragments or powder of broken chondrules. Sponge-like masses
of nickel-iron alloy (constituting on average about 12% of the meteorite by weight) and inclusions of troilite are
found in the matrix of the chondrites.
The iron-stones, including the so-called pallasites, consist of spongy masses Of iron with included chondrules
of silicates (mainly olivine and enstatite).
The irons contain on the average about 8% of
nickel. The most common inclusions in them are troll-
ite-FeS, Schreibersite (Fe, Ni)313, etc.
TABLE 1
Falls and Finds of Different Types of Meteorites
Type of meteorite
Finds
Falls
number
Iron
409
29
iron-stone
46
6
Stone
165
547
Total
620
582
The main mass of iron in meteorites exists in two
phases ? kamacite and taenite, and this determines the
structure and composition of iron meteorites (Fig. 3).
The following brief statistics compiled some time
ago by Watson show the relative proportion of different
meteorites and give an idea of their durability under
terrestrial conditions (Table 1).
We shall turn now to the isotopic constitution of a number of elements in terrestrial igneous rocks and in
meteorites.
Three processes which lead to the variation in the isotope ratios in igneous rocks and meteorites may be
mentioned:
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Fig. 1. Chondrules from a meteorite (Nikol'skoe) Fig. 2. Chondrules. Under the microscope in trans-
(x4.5).
milted light (x 20).
111111111111111111111
0 4 2 0 4 5 6 7 6 410
Fig. 3. A fragment of iron meteorite (Sikhote-Alin'). View of the surface.
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1. Radioactive decay of uranium, thorium, 1 30.
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The effect of additives. A comparison of the work reviewed does not lead to any definite conclusion re-
garding the effect of surface active substances on the heat transfer to liquid metals. The experiments with mer-
cury-magnesium amalgams, conducted by Korneev, and the experiments of Stromquist with mercury including
additions of sodium, did not show any effects of the additives on heat transfer. However, the data of Doody and
lounger, conducted at the same Peclet numbers, indicate that the addition of sodium to mercury noticeably im-
proves heat transfer. The experiments of Lubarsky, Borishansky and Kutateladze on the addition of magnesium
to a eutectic of lead-bismuth did not lead to any noticeable improvement in heat transfer. The data of Unter-
mejrer indicate a considerable improvement in heat transfer. A comparison of experiments for determination of
surface material effects on heat transfer leads to the conclusion that in a qualitative sense heat transfer apparently
is higher in those cases where the metal wets the heating surface. However, it is not possible at this time to make
i quantitative evaluation of this effect.
The following equations may be recommended for calculation of heat transfer to liquid metals flowing in
standard tubes [5, 7]:
Nu= 3,3+ 0,014Pe?,8,
Nu= 5+ 0,0021Pe.
,(15)
(16)
In these equations 300 < Pe < 15,000, and Re > 10,000.
In the region of low peclet numbers, Pe = 20 to 300, calculations may be carried out by the approximate
equation following, until more detailed data is obtained:
Nu= 0,7Pe'/3. (17)
For sodium (with tube surface wetting and very clean equipment) in the region of Peclet numbers 100 to
1400 the following equation may also be used [21]:
Nu= 5,9 +0,015Pe?,8. (18)
The above discussion applies to average heat transfer with fluid flowing in long tubes. A number of inves-
tigations have been concerned with heat transfer in fluids flowing through short tubes. A,comparison of the re-
sults of many investigations with the results of theoretical calculations has been made by Lubarsky and Kaufman
[17]. It has been established that heat transfer in the entrance region is higher than it is after flow has been sta-
bilized. As a first approximation it may be assumed that at L/D > 30 the effect of the entrance region on average
heat transfer is low. For short tubes a correction factor according to Kondrat'ev and Mikheev [8] may be used
as follows
(19)
Heat Transfer to Liquid Metal Flowing in Flat Channels
Annular ducts. Experiments with mercury and a eutectic of lead-bismuth included the interval of Peclet
numbers Pe = 45 to 1700. In experiments with sodium and an alloy of sodium-potassium this interval was Pe =
= 10 to 1000. A comparison of all this data, shown in Figs. 5 and 6 allows as a first approximation, the use of
the equations for circular tubes given above with equivalent hydraulic diameter used in place of tube diameter,
De = D2 Di = 26 where 6 is the width of the channel.
Flat ducts. Heat transfer in flat channels, using mercury, was measured by Sinich [17] and using an alloy
of sodium-potassium it was measured by Tidball [22]. The experiments were conducted in the range of Peclet
numbers Pe = 300 to 1000 and yielded values of Nu = 4-5 (Figs. 5 and 6). When the wall temperature was con-
stant the value of the constant term in the expression for Nu was somewhat lower than when q = const.
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Nu-a(r)
10
8
6
2
73
te-
4
6
5
3
2
1,6
3 4
6 8 101
2
4
6 8 10 3 2103
)
Pe = a
Fig. 5. Heat transfer for heavy metals (mercury, lead-bismuth) flowing through
channels. L/De > 30. Results of experiments with mercury: 1) Stirikovich, Sorin
and Semenovker; 2) Korneev (D2/D1 = 1.35); 3) Mikheev, Fedinskii (D2/D1 = 1.55);
4) Trefethen (D2/D1 = 1.4); 5) Trefethen (D2/D1 = 1.75-2.31); 6) Sinich (flat chan-
nel, 6 = 6.3 mm). Results of experiments with eutectic of lead-bismuth: 7) Lu-
barsky (D2 /D1 = 1.25).
6
2
1
6
21
5
n
9 A
R int 9 t
6 8 M
Pe -W011-0,)
Fig. 6. Heat transfer for light metals (sodium, sodium-potassium) flowing in channels.
L/De > 30. Results of experiments using an alloy of sodium-potassium: 1) Lyon (D2/D1 =
= 1.37, 1.43); 2) Lyon (D2/D1 = 1.23); 3) Werner, Kling, Tidball (D2/D1 = 1.83? steel);
4) same, nickel; 5) Hall, Kraft and Jenkins; 6) Tidball (flat channel) initial results;
7) same, final results. Results of experiments with sodium; 8) Hall, Kraft, Jenkins(D2/D1 =
= 1.25).
Heat Transfer in Flow of Liquid Metal Coolant Along the Length of a Bundle of
Rods
The order of magnitude of the numbers that characterize heat transfer when liquid metal coolant flows
along the length of a bundle of rods may be derived from data on the heat transfer coefficients cited by Tidball
[22], Schwenk and Shannon [23], Rosenblatt and Brooks [24]. The empirical equation proposed by Brooks and
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Rosenblatt should be used only with great caution, since it is accurate only for conditions that are close to the
experimental conditions under which it was obtained.
The authors (Brooks and Rosenblatt) recommend the equation
aD
s = 612 ( WDSt ) 6 ( 1,2
a '
(20)
where Dt is the external tube diameter; S is the cross sectional area of flow between the tubes in the bundle;
F is the heat transfer surface area; a is the heat transfer coefficient.
The heat transfer obtained when liquid flows over a plate surface, with channel width infinite, is determined
through the integral equations for boundary layer.
In liquid metals the Prandtl number is much less than unity (Pr ? 1) and 6 T> 6, where 6 T and 6 are
the thermal and hydrodynamic boundary layer thicknesses, respectively. In the region where D < y < 6 the
velocity component wx varies in accordance with usually accepted laws for the hydrodynamic boundary layer
of an incompressible liquid.
In the region y > 6
wx wo = const.
A solution for a laminar boundary layer may be obtained by introducing the usual approximate profiles of
velocity and temperature represented by fourth-power polynomials.
a L
For Nu = where L is the length of plate, the following equation may be used with satisfactory accuracy
X
Nu =1,111(1= fir113) Pe, (21)
where Pe = 1-1111 .
a
For a turbulent boundary layer Kutateladze and Fedorovich have developed two limiting methods.
In the first method a linear distribution of tangential pressures and thermal currents was assumed through
the boundary layer thickness, while the 1/7 power law was used for velocity distribution. The turbulence in the
region 6 < y < 6 T was assumed equal to zero.
Over the range 103 < Pe < 2.105 a third approximation is expressed by the equation
Nu = 0,38Pe0,65. (22)
In the second calculation a linear distribution was assumed in the range 0 < y 2 -107.
In the experiments of Hymen, Bonilla and Ehrlich the tube diameter had an effect on this transition.
The analysis of the experiments, that was run by Fedinskii, indicated that in Eq. (29) the quantity(Pr) co
practically coincides with the right side of Eq. (27). Therefore it may be considered with sufficient accuracy for
practical purposes that for all media the following equation applies:
Pr2Gr
Nu = ito 1+ Pr j ?
(30)
When the vapors of liquid metals are condensed the condensate deposits out either in the form of droplets
or in the form of a continuous film. For metals as contrasted to other substances the droplet type of condensation
Is the more characteristic. In addition the thermal resistance of the condensate film, when it forms, is extremely
small.
This is explained by the fact that the high heat conductivity of the metal vapors leads to a basic redistri-
bution of thermal resistances of the condensate itself and of the diffusion area near the surface of the condensate.
Because of this the supposition, common in the theory of film condensation, that the temperature at the surface
of the film is practically exactly equal to the saturation temperature at the center of flow channel, is not justi-
fied in the case of metal vapor condensation.
TABLE 2
Heat Transfer During Condensation of Sodium Vapors
Saturation temperature t, ''C
631
725
866
Heat flux q, kcal/nn2?hr
1.5?105
1.92.105
2.66.105
Coefficient of heat transfer a, kcal/m2?hr:
experimental results
results from film condensation equa-
tion on the assumption that tf = t"
5.55.104
84.5 ? 104
5.85 .104
74.0-104
6.50.104
61.2 ? 104
Calculations indicate that when Pr ?> 0 turbulence leads to a certain increase in thermal resistance of the
condensate film, and not to a decrease, as is the case for nonmetallic liquids.
In Table 2 are shown some data from Bonilla and Meysner on heat transfer under conditions of sodium vapor
condensation.
Thus, experiment confirms that the thermal resistance of the condensate film proper is extremely small.
It follows that the type of condensation has little effect on the heat transfer in the case of liquid metal vapors.
The diffusion theory of heat transfter under conditions of droplet condensation leads to the conclusion, that
for this case
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(31)
where n ci 0.5.
According to the experiments of Gel'man, when mercury vapors condense an even more sensitive depen-,
dence applies;
1,2.105 )77) 3 V r I ? w?
a = -1
At
(32)
where 2 is the pressure in atmospheres absolute; y? w" are the weight flow velocities in kg/m2. sec.
The boiling of metals, in general, conforms to the same laws as the boiling of nonmetallic liquids.
In Fig. 8 are shown the relationships of heat transfer coefficient on the temperature potential for the boil-
ing of water and for the boiling of an amalgam of magnesium and mercury over a horizontal tube under condi-
tions of free convection (surface boiling, with the surface immersed in a large liquid volume). For both metallic
and nonmetallic liquids the nature of the relationship under investigation is identical.
Poor wetting by the coolant of theheating surface leads to an earlier initiation of film boiling. When the
liquid does not wet the heating surface then film boiling for all practical purposes exists steadily at any heat flux
densities.
Addition to the liquid of surface-active substances may change the degree of wetting of the surface. For
example, the addition of an insignificant quantity of magnesium to mercury or of an insignificant quantity of
sodium, significantly improves the contact between the liquid and steel. This is particularly noticeable in boil-
ing heat transfer because of the basic effect of the degree of wetting on the character of the flow of a vapor-liquid
mixture.
, kcal/m2 ? hr
3.104
8
4
2
103
6
4
3
3 4
/*---%?\
6 8 10
1 4 6 8 le 2 4 6 810'
dt-t"-t,?C
Fig. 8. Heat transfer for boiling of an amalgam of mercury and for boiling of water in a large
liquid volume. 1) Magnesium-mercury amalgam; 2) water.
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The effect of wetting on the hydraulic resistance to the flow of a vapor-liquid mixture was studied for flow
of boiling mercury. In vertical tubes the motion of two-phase current averaged over a sufficiently long period
of time, always possesses axial symmetry. In inclined and horizontal tubes this occurs only at high flow velocities.
When the velocities are not high the flow separates into layers (the lower portion 'Of the tube perimeter is im -
mersed in liquid while the upper portion is in contact with vapor), and this decreases cooling of this surface. When
the flow has not separated into layers or when the separation is not well developed the distribution of the liquid
and vapor phases depends basically on the degree of wetting of the tube surfaces by the liquid. A liquid that ad-
heres to the walls forms a continuous film on the surface thus ensuring a high cooling rate with nucleate boiling
regime. The vapor thus formed flows away into the center of the flow channel.
1,0
0.8
0.6
0,4
0.
-
IV el
? = 20
..-
..--
------
--. ------
-- --
t i / 2
....14
D
-- -- ?.
_ ? a
/ /
/ ....
---.."
/ / ...-
/
?S
,?
.--
/
/
/
/
/
/
/ /
../ /
..-
.../
---
/
/
2
6
8
12
_q
Wo
Fig. 9. Cross section portion filled with mercury vapors in a vertical tube. ?) Mercury at a
pressure of 5-15 atmos; ---) water at a pressure of 5 atmos.
When the liquid does not wet the tube surface (for instance, in the case of mercury flowing through glass
or steel tubing) the vapor bubble motion is reversed; vapor bubbles separate out between the tube wall and the
liquid steam. At the center of the flow channel there is essentially only liquid moving in a pulsating stream
[26].
The change in the composition and distribution of a two-phase stream, as a function of wetting of the walls
by the liquid, does not significantly affect the hydraulic flow resistance, although it basically affects heat trans-
fer. This is because the integral hydrodynamic characteristics of a two-phase flow depend on the volumetric con-
centrations of the phases and are affected but little by the detailed stream composition. In connection with this
it may be noted that the flow characteristics of a vapor?liquid mercury mixture are near the water-steam mix-
ture characteristics.
In Fig. 9, the basic hydrodynamic characteristic is given from the data of Gremilov [27] in terms of one
coordinate (the volumetric vapor concentration) and the other coordinate w'/w0 (the ratio of the vapor velo-
city to liquid velocity). The parameter used was the Froude number 4/D stated to an accuracy corresponding
to g = 9.81 m/sec2, where D is the internal tube diameter. The number was constructed from steam-water data
and from mercury-mercury vapor data flowing in vertical tubes.
When a liquid that does not wet, the tube surface boils, heat transfer may be improved by increasing the
frequency of flushing the tube.
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es6
50
Cs
30
20
5
4
2
0,5
0,4
0,3
0,2
7
6
1
4
5
3 5 6 8 10
20 30 40 60
100 2003 500
q? 10 kcal/m2 ? hr
Fig. 10. Heat transfer with boiling of various liquid
metals in large volumes. 1) Magnesium-mercury
amalgam in vertical tubes; 2) magnesium amalgam
of mercury flowing over the exterior of a tube; 3) film
boiling of an amalgam of mercury; 4) boiling of pure
mercury; 5) boiling of cadmium; 6) boiling of an alloy
of sodium-potassium; 7) boiling of sodium.
a40-3kcal/m2 hr
20
10
9
8
7
6
5
4
According to the data of Lozhkin and Kanaev [3],
' when mercury boils in a tube that has a spiral insert of
strip iron, the percentage of flushing of tube surfaces by
liquid reached ? 70% as compared with 12-20% in
the absence of this turbulence generator.
Figure 10 shows the dependence of a on s when
liquid boiling in certain metals occurs over a large
volume [6, 28, 29]. For metallic liquids that wet the
heating surface (sodium, potassium-sodium alloy, mag-
nesium amalgam of mercury), in the region of heat
fluxes q < qcr the usual relationship between coefficient
of heat transfer and heat flux density holds true, a =
Aqn, where n =1 0.7.
For liquids that do not wet the heating surface
(mercury, cadmium) the values of a that apply are
characteristic for film boiling regime.
Figure 11, which shows the results of the experi-
ments of Korneev [14] with a mercury-magnesium amal-
gam, indicates that the rate of heat transfer in nucleate
boiling is practically independent of the concentration
of magnesium. However, the transition to film boiling
occurs at various heat fluxes ger as a function of mag-
nesium concentration.
It is well known that with fully developed
nucleate boiling the coefficient of heat transfer
depends very little on the liquid flow veloc-
ity [30]. Data on boiling heat transfer
G.,
.
?
0
,
1
I
0
000
.
D0
4

4
0
? !' ?,,
? ,,a
A
a g 11
.
.-.-.
a p A
..
0
0
aces
0
...
1
?
d3
? .
.
?0-
o?.
I
o
o
cx=5,62 q 467
0
U
1
In 2 4
6
8 102 2
3 4 5.10'
q? t0-3 kcal/rha .hr
Fig. 11. Heat transfer with nucleate boiling of magnesium-mercury amalgam. Percen-
tage of magnesium: El) 0.01%; A) 0.03%; 0) 0.04%.
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,of magnesium amalgam in free convection within a large volume and in natural convection in a tube are close
to each other and confirm this assertion for liquid metals.
When the liquid does not wet the tube surface ,this statement no longer is true. There is evidenced a basic
influence by the flow velocity wo and by the tube diameter D. A certain decrease of the value of a as a in-
creases is noted [1, 2, 12].
When a mercury amalgam boils in horizontal tubes the coefficient of heat transfer is not uniform around
the tube circumference. A decrease in heat transfer at the upper part of the tube depends on the heat flux den-
sity, which creates an increase of steam content in the upper part of the unsymmetric, two-phase fluid stream.
The velocity w0,1 after which heat transfer in the upper part of the tube remains at a constant high level, may
be determined through the empirical equation [14];
w; 22.10-5 q0,62 D0.76 in/ see.
Here q is measured in kcal/m2 D in mm.
When wo' > W6',1the heat transfer coefficient is determined by the empirical equation
cc= 12q?,67 Zeig'3 (34)
These equations have been checked at 5000 < q 70,000 kcal/M2-hr, 13 < D < 40 MM; 1 < p < 120 atmos
and 1 wo < 19 m/sec.
(33)
LITERATURE CITED
[1] M. A. Styrikovich, I. E. Semenovker and A. R. Sorin, Sovetskoe Kolotyrbostroenie 9, 316 (1940).
[2] M. A. Styrikovich and I. E. Semenovker, J. Tech. Phys. (USSR) 10, 16, 1324 (1940).
[3] A. N. Lozhkin and A. A. Kanaar, Binary installations tin RUstiati](MAShGIZ, 1946).
[4] A. A. Kanaev, Sovetskoe Kolotyrbostroenie 2, 18 (1953).
[5] V. M. Borishanskii and S. S. Kutateladze, EnergomashinOstroenie 6. 5 (1957); 4 (1958).
[6] S. S. Kutateladze, Basic Heat Transfer Theory [in Rutsian] (MAShGIZ, 1957).
[7] M. A. Mikheev, V. A. Baum, K. D. Voskresenskii and 0. S. Pedinskii, Coll; Reactor Building and
Reactor Theory [in Russian] (lzv. AN SSSR, 1955), p. 139.
[8] M. A. Mikheev, Heat Transfer Principles [in Russian] (Gosenergoizdat, 1956).
[9] L. I. Gel'man, Teploenergetika 3, 47 (1958).
[10] H. E. Brown, B. H. Amftead, and B. E. Short, Trans. ASME 79, 2, 279 (1957).
[11] S. E. Isakoff and T. B. Drew, General Discussion of Heat Transfer, Inst. Mech. Eng. and ASME (1951).
p. 405.
[12] R. C. Martinelli, Trans. ASME 69, 8,947 (1947).
[13] R. E. Lyon, Chem. Eng. Progr. 47, 275 (1951).
[14] M. I. Kornev, Teploenergetika 4. 44 (1955); 7, 39 (1955).
[15] D. English and T. Barret, General Discussion of Heat Transfer, Inst. Mech. Eng. and ASME (1951), p7 458.
[16] T. C. Doody and A. H. lounger, Chem. Eng. Ptog. Symposium Ser. 5, 33 (1953).
[17] B. Lubarsky and S. J. Kaufman, "Review of experitnental investigation of liquid rittal heat transfer,"
Report NACA No. 1270 (1956).
[18] H. A. Johnson, W. J. Glabaugh and J. P. Hartnett, trant. ASME 75, 6, 1191 (1953); 76, 4, 505 (1954).
570 '
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Declassified and Approved For Release 2013/09/13: CIA-RDP10-02196R000100010004-9
[19] E. R. Gilliland, R. J. Musser and W. R. Page, Coll: General Discussion of Heat Transfer (1951), p.402.
[20] L. M. Trefethen, Coll: General Discussion of Heat Transfer (1951), P. 436.
[21] I. I. Novikov, A. N. Soloviev, E. M. Khabakhpasheva, V. A. Gruzdev, A. I. Pridantsev and M. Ia.
Vasenina, Atomnaia Energiia No. 4, 92 (1956).
[22] R. Tidball, Chem. Eng. Progr. Symposium Ser. 5, 233 (1953).
[23] H. C. Schwenk and R. H. Shannon, Power 99, 11, 92 (1955).
[24] R. D. Brooks and A. L. Rosenblatt, Mech. Eng. 75, 5, 363 (1953).
[25] S. C. Hymen, C. T. Bonilla and S. W. Ehrlich, Chem. Eng. Progr. Symposium Ser. 49, 5, 21 (1953).
[26] A. N. Lozhkin, Kroll.', J. Tech. Phys. (USSR) 8, 21 (1938).
[27] D. I. Gremilov, Coll: "Combined power stations and power cycles," Trudy TsKTI 23. 86 (1952).
[28] R. E. Lyon, A. S. Foust and A. L. Katz, Chem. Eng. Progr. Symposium Ser. 49, 5, 21 (1953)N
[29] Liquid Metals Handbook, sodium (NaK) Supplement (Washington, 1955).
[30] Coll: Heat Transfer Problems with State Changes [in Russian] (Gosenergoizdat, 1953).
Received November 4, 1957
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EVALUATING THE ECONOMIC FEASIBILITY OF USING SPECIAL
HEAVY CONCRETES FOR RADIATION SHIELDING
A. N. Komarovskii
The first part of this article is a survey of the work of foreign authors
dealing with the economics of using various concretes for biological radia-
tion shielding at nuclear reactors and at charged particle accelerators.
Several of these authors affirm that it is economically justifiable to use
heavy concretes for these purposes. However, others advocate the use of
common concretes with mineral aggregates. The second part of the article
gives the results of corresponding economic analyses conducted in the USSR.
These analyses lead to the conclusion that the use of special heavy concretes
is justifiable only in exceptional cases.
The authors of a number of works dealing with biological radiation shielding note the advantages of special
heavy (including iron ores and iron scrap) concretes, as well as the advantages of barites concretes over common
concretes with mineral aggregates. Greutz and Downes [1] conclude that it is economically justifiable to use
more expensive magnetite concrete for particle accelerators, because in view of its high density (3.9 tons/m3)
there is less floor area required for the same amount of shielding. Beck and Homer [2] reach the same conclusion.
Callan in [3], a paper devoted to concrete shields for nuclear reactors, notes that in many cases (for exam-
ple, small reactors) heavy concrete including special aggregates is better than common concrete despite the high
cost, since the heavy concrete shield can be made thinner.
Lane [4] recommends the use of concrete shielding weighing 3.5 to 4 tons/m3 for high power reactors,
while Stephenson [5] states that the best heavy concrete for reactor or isotope storage shielding is barites con-
crete.
On the other hand, there are convincing arguments for the use of common concrete using local aggregates,
but this does not exclude the use of special concretes in details of the shield or when over-all dimensions must
be kept low.
Thus, the American firms "Pacific Gas and Electric Co." and "Bechtel Corp." that are designing large
dual-purpose reactors of 500 mw thermal power, note in their report to the Atomic Energy Commission of the
USA [6] that there are no economic advantages in favor of high density concretes. The same is stated in analo-
gous reports by other companies (Monsanto Chemical Co. and Union Electric Co.) that participated in the design
of large power reactors. These companies decided to use common concrete in their reactor installations.
Glen [7], summarizing the shielding design experience at the Oak Ridge National Laboratory (USA) notes
that the thickness of shielding around a stationary reactor in contrast to the shielding around a small reactor, is
not a significant factor, since decreasing the cost of shielding around a stationary reactor is far more important.
Price, Horton and Spinney [8] in their summary of shield design experience state that special heavy con-
cretes using metallic or ore aggregates cost ten times as much as common concretes. This high cost of heavy
concretes necessitates very careful treatment in selection of its constituents and handling methods, while the high
density makes it impossible to use common building fixtures and complicates pouring and setting the concrete.
These factors are significant for the totarcost of the reactor shield. The authors also note that the use of steel
573
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scrap and in particular steel shot in concrete is feasible only in those cases when design requirements call for
very compact shielding. For example, the use of special heavy concrete in the upper shield of the English re-
search reactor DIM reduced the length of fuel element assemblies and made possible the use of convenient
handling tools for their removal (the cost advantages thus realized were greater than the additional costs of the
special concrete). The authors make the general conclusion that common concrete is one of the cheapest shield-
ing materials while costly heavy concretes can yield economic advantages only in shielding of small sized reac-
tor cores.
TABLE 1
Economic Characteristics of Some Concretes (Data from Institute of Atomic Energy of the Academy of Sciences,
USSR)
Type of
concrete
Density,
tons/m3
,
Shielding
effective-
ness, 97o
Cost
rubles/m 3
Cost normalized
to unit effect-
iveness
rubles/me
Economy,
rubles/m3
.
Cost
increase,
'
rubles/m
Common concrete
Sand concrete without
coarse agvegates
Concrete with iron
ore
Concrete with metal
scrap
,
2,2
2,0
2,2
5,5
100
I
90
150
250
350
180
700
2000
350
200
470
800
150
-
-
120
450
In the work mentioned above, [5], it is also noted that since the cost of steel is high in comparison to other
materials used in concrete (in addition, stratification may occur in such concrete) the use of metal aggregates
in concrete shields is usually not justifiable.
The results of studies conducted in the USSR point to the use of common concretes. Thus both design and
analysis work conducted at the Institute of Atomic Energy of the Academy of Sciences, USSR indicates that the
exterior walls of accelerators as well as of some reactors should be made of concrete using locally available
aggregates, and that no attempt should be made to make wide use of special heavy concretes. Some results of
this study are shown in Table 1.
TABLE 2
Costs of Metallic Rubble, Shot and Ores in Various Parts of the USSR (with transportation costs included)
Material
Unit of-
measure
ment
Cost in rubles
Central
region
Central
Urals
,
Southern
Urals
Western
Siberia
Eastern
Siberia
Metal rubble .
6 6 6' 6' 6' El 6' 6' 6' 6' rt rt 00
oo
760,08
757,80
758,22
761,46
793,19
Metallic shot, 6 mm diameter
714,96
763,25
756;17
812,97
850,63
Iron ore (magnetite
or hematite)
128,85
71,75
72,90
100,72
146,95
Rubble made of this ore
134,45
76,68
78,13
106,32
152,55
Sand extracted from this ore
158,45
104,84
106,29
130,32
176,55
Iron ore (limonite)
100,11
101,13
102,89
178,52
234,37
Rubble extracted from iron (limonite) ore
105,71
106,73
108,49
184,49
239,97
Sand extracted from iron (limonite) ore
129,71
130,73
132,49
208,12
263,97
Barite ore
464,30
389,41
383,61
339,18
398,68
Rubble from barite ore
469,90
395,01
389,21
344,78
404.,28
Sand from barite ore
493,90
419,01
413,21
368,78
428,28
Mineral sand
29,30
41,40
33,90
33,90
35,50
Common rubble
53,80
59,40
65,00
53,90
62,90
5'74
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?S(1)
4-4
bo
ce?)
scinicu
a)
UZI
bo
tz;
ta.
-4
H
Total cost of building 1
and shielding, 0/0 I
vliaqi
-asvg
0 c-4 cz
--
uliaqi?
ma
-2sam
lion-
. Iva
sin
auT2.
Iva
-uaD
0 " o c--.,
c -44 \V V..,
?'?,-1
."
c
Cs
8 - -8 I ? gi
ss ? ssi
?
CD
8 to co
C. . o Fo
co

0/0 'amnion
.Sulpunq Jol
-0Va.1 IMO"
, 10
C CC 10
._,' c.. cc,
a) a:
1,a,
cD
Cost of concrete shield-
ing,
EiliaUCIal.
-isvg
. n I ?
st
ula
-isam
spin
1.?
:-uao
co .,
8 If) i .,,.
??
C"
00
C0Cn
CD co ,.. .
c, , , ,,
--cs, C \I
"
00
,I.
CO
Cs
. E., CO
CO
Cs
uo0a
I'M
-PO
oo co c'1
c=, c?i cocq
'-' ,-, -. cq
U).
CO
Average cost of 1 m3
of concrete, rubles
? Uq11;
-1SE3
0I0
-Jsaivi
sIvill
. ten
-uaD
u-Ty-F1
l'en
sUOD
CS to 0
Cs
Cs I 0
It)
c.i
0
l0
co
c?i
s c) co ?
o o -.
co-...1. c.t) 4---
--, --, cq
c.,
-,
t--
cq
co o to
Ki N. c.?
cq
cl
In
.4.,
? c,,
c..,
, ? cm
-,:, ? Cu,' CT -.
5' Cs --.
C'0
C \I
CD
s--t
CO
C\1
N,..!. en
F.4 ..... M
0 (I) G
0 -0 2
M 1" CD CNI., r.
.....4 C',.; co- ? ,14 1 L.,1
Concrete aggregates
Mineral sand and rubble (98%), iron
ore and iron scrap (2%)
Mineral sand and iron ore (magne-
tite or hematite)
Iron ore (magnetite or hematite)
Fine iron ore (hematite or mag-
netite) and metal scrap (64%)
mineral sand and rubble (36%)
Mineral sand and iron scrap
In 1956 a study was made of the economics of
using various concretes in various parts of the USSR for
shielding of large reactors. Various shield designs were
examined for various concrete compositions. This made
possible the calculation of total concrete volume re-
quired with different types of concrete, the calculation
of the extent of the work required to erect the buildings
and the assembly of cost figures for comparison of each
of the design alternatives, with all costs incident to a
reactor installation considered and not only its shield-
ing costs (as was done in all work published previously).
The following types of reactor installation shields
were considered:
? shielding, 98% common concrete by volume
(y = 2.3 tons/m3) and 2% special heavy concrete (y =
= 4.4 tons/m3);
? shielding made of special heavy concrete (y =
= 3.0 tons/m3) using common sand and coarse iron ore
aggregates;
? shielding made of special heavy concrete (y =
= 3.6-tons/m3) using both coarse and fine iron ore aggre-
gates;
? shielding part of whose volume (the reactor
shield proper) is made of special heavy concrete ( y =
= 4.2 tons/m3) using fine iron ore aggregate and coarse
iron scrap aggregate, while the rest of the volume (the
walls of the central reactor chamber, etc.) is made of
common concrete (y = 2.3 tons/m3);
? shielding made of special heavy concrete (y =
= 4.2 tons/m3) using mineral sand and both coarse and
fine metal scrap aggregates.
In assembling the cost data for special high den-
sity concrete the following material availability data
was used; iron ore for the central region was obtained
from Krivoi Rog, iron ore for the central Ural region
was obtained from Goroblagod, and for Siberian regions
was obtained from Kuznetsk; metal rubble for the cen-
tral region was obtained from a factory inYaroslavl, for
the central Ural regions was obtained locally, and for
the Siberian regions from a factory in Novosibirsk.
The costs of these materials (Table 2) were ob-
tained through realistic estimates and FOB prices ob-
tained from purchasing agents; the costs of transporta-
tion-weie obtained from actual conditions as they existed
throughout 1957.
The basic data from the estimates are given in
Table 3. On the basis of these estimates the following
conclusions may be made:
1. The use of special heavy concretes using iron
ore aggregates, and also the use of concretes with coarse
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aggregates of iron ore and fine aggregates of mineral sand, in the biological shielding of reactors, results in rela-
tively low (1-120/0) construction cost increases as compared to the costs of a building in which common concrete
only is used.
2. The use of metal scrap for the coarse aggregate increases the cost by 28-33% when the heavy concrete
Is used for the shielding of the reactor proper only, and increases the cost by 60-72% when the heavy concrete is
used for the central chamber shield,
TABLE 4
Comparative Figures on the Concrete Shielding of the Circular Accelerator of '7 Bev (for the central region of
the USSR)
Concrete aggregates
Concret
density,
tons/m3
Volume of
concrete in
the shield
Reduction
in size
ctgell
area
m2
in build
when spe-
vcsn-
. - .
volume
1113
Cost of building
and shield
millions
of rubles
%
coarse
fine

M3
'l?
ineral rubble
Mineral sand
2,3
13 024
100
?
?
43
100
Iron (hematite) ore
Mineral said
3,0
10 024
76,5
545
3 790
43,18
100
Iron (limonite) ore
Iron (limonite) ore
3,0
10 024
76,5
545
3 790
43,22
100
arite ore
Barite ore
3,1
9 775
?
540
3 874
48,1(3
112
Iron (hematite) ore
Iron (hematite) ore
3,5
8 138
62,5
547
5 000
43,13
100
Iron scrap
Iron (hematite) ore
4,4
6 837
52,2
666
6 222
48,16
112
.
TABLE 5
Comparative Figures on the Concrete Shielding of the Linear 35 Mev Accelerator (for the central region of the
USSR)
Concrete aggregates
Concrete
density,
tons/m3
Volume of
concrete in
h ld
Reduction
pg size when
uggy concretes
--ar2eu
m
in build-
4pecia1
are
.vbIlirrie-
n113
Cost of building
and shield
coarse
fine
m3
%
,
millions 1 0,
of ruble f '
.
Mineral rubble
Mineral sand
2,3
15 100
100
.
?
?
18 678
100
Iron (hematite) ore
Mineral sand
3,0
11 500
76
315
4 493
19 419
115
Iron (limonite) ore
Iron (limonite) ore
3,0
11 500
76
315
4 493
20 024
119
Barite ore
Barite ore
3,1
11 053
73
337
5 040
26 863
160
Iron (hematite) ore
Iron (hematite) ore
3,5
8 400
56
370
5 095
21 027
125,5
Iron scrap
iron (hematite) ore
4,4
7 876
52
457
5 754
28 476
172
Thus in any case, it is better to use common concrete for the biological shielding of reactors. A possible
exception is when the reactor is built near a source of inexpensive heavy ores, as well as in the construction of
extremely complicated and expensive foundations and reactor bases, when a reduction of the shield dimensions
by use of special heavy concretes may change somewhat the cost figures in favor of the heavy concretes.
The economics of using heavy concretes for shielding of reactors that are enclosed in gas tight steel shells
whose cost and volume decrease with increasing concrete density (as a result of decreasing shield size) require
additional investigation. However, preliminary estimates indicate that in these cases as well, the total cost of
erection of a stationary reactor with common concrete shielding is lower than the cost of a reactor with special
heavy concrete.
576'
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Analogous study was made on the economics of using special heavy concretes for the biological shielding
around a 7 Bev synchrophasotron and a 35 Mev linear accelerator. The erection costs were estimated for the con-
ditions of the Central region, and designs and cost figures were assembled for different types of heavy concretes.
This work was conducted in accordance with the methods outlined above. A comparison was made of total
building costs for the entire accelerator facility under the following versions of shielding;
? shield of common concrete ( y = 2.3 tons/m3);
? shield of concrete with coarse (Krivoi Rog hematite) and fine (mineral sand) aggregates (y = 3 tons/m3);
? shielding of concrete with coarse and fine aggregates of Lipets limonite ore (7 = 3 tons/m3);
? shielding of concrete with coarse and fine aggregates of Salair barites ore ( y = 3.1 tons/m3);
? shielding of concrete with coarse and fine aggregates of Krivoi Rog hematite iron ore (y = 3.5 tons/m3);
? shielding of concrete with fine aggregate made of Krivoi Rog hematite iron ore and coarse aggregate of
metal scrap (y = 4.4 tons/m3).
The basic figures of these estimates are,given in Tables 4 and 5.
This work has made possible the following conclusions;
1. The use of special heavy concretes in the biological shielding around large circular accelerators does
not yield any economic advantages by comparison with common concrete, but does not produce any noticeable
cost increases either; concretes including barites ores and metallic scrap, whose use increases shielding costs
by approximately 12%,are an exception.
2. The use of special heavy concretes for shielding of large linear accelerators increases building costs
by 15-20%, and the use of concretes with barites ores, up to 60%, while metallic scrap concretes increase costs
by up to 72%.
If all that has been presented above is taken into account together with the difficulties in obtaining and
transporting special aggregates for heavy concretes, as well as the complexity of preparing the concretes, then
the general conclusion may be reached that the use of special heavy concretes for shielding nuclear reactors and
accelerators is not justifiable either technically or economically.
An exception may be the case where the reactor building is situated near a source of iron ores. The use of
heavy concrete may prove to be justified for over-all shielding or for shield details around nuclear reactors and
accelerators in the following circumstances;
? when the reactor or accelerator are housed in a small building and it is essential to reduce shielding di-
mensions to fit the equipment into the available space;
? when it is essential to reduce the lengths of experimental openings (for example, collimating openings
in accelerators);
? if the shield thickness required with common concrete reduces the angle of vision of the operator or the
experimenter (through viewing windows);
? when it is essential to maintain a constant shielding worth over the entire shield area, even with local
thickness reductions (experimental openings, gas and water ducts, etc.);
? when it is necessary to erect very complicated and expensive bases and foundations for the installation,
when a reduction of over-all shield size through the use of special heavy concretes will change the cost relation-
ships so as to favor the heavy concretes.
LITERATURE CITED
[1] E. Greutz and K. Downes, Appl. Phys. 20, 12 (1949).
[2] C. Beck and C. R. Horner, Concrete 63, 2, 11 (1955).
[3] E. Callan, Concrete Inst. 25. 1 (1953).
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[4] J. A. Lane, Nucleonics 13, 6, 57 (1955).
[5] R. Stephenson, Introduction to Nuclear Engineering (Gostekhizdat, Moscow, 1956)."
[6] "Industry teams report on A-power," I-II, Chem. Eng. 60, 7, 8 (1953).
[7] H. M. Glen, Oak Ridge National Laboratory, "Material of biological shielding," 2nd Nuclear Engineer-
ing and Science Conference, March 11-14, 1957, Philadelphia.
[8] B. Price, C. Horton and K. Spinney, "Radiation shielding,' Atomic Energy Research Establishment,
Harwell, 1957.
Received December 14, 1957
? Russian translation.
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DEFORMATION SYSTEMS OF a-ZIRCONIUM
Iu. N. Sokurskii and L. N. Protsenko
The deformation systems of a-zirconium iodide have been studied in
coarse-grained polycrystalline specimens deformed by upsetting. The orien-
tation of the grains was determined from Laue patterns obtained in a special
back-reflection camera using a small-diameter beam. The indices of the de-
formation systems were determined by the two-surface method and by the
pole locus method.
It was found that a-zirconium is deformed by slip along the (1010)
plane in the [1E10] direction and along the (1011) plane. A number of
twinning systems have been discovered in a-zirconium: a) K1 (101.2), ni
[1011], K2 (1012), m [1011] and s = 0.173; b) K1 (11-21), ni [1126], K2
(0001), Ti2 [1120] and s = 0.629; c) K1(1122), ni [1123] and in one case,
d) K1 (11-2.3), 711 [1122].
It is known that 8- zirconium is very plastic, much more plastic than other metals with a hexagonal lat-
tice. The plasticity of a material is determined by a number of factors, in particular by the type and number of
the deformation systems. The literature contains no exact data on the deformation systems of zirconium, with
the exception of a few brief statements in the book by Lustman and Kerze [1].
In the case of titanium, which is analogous to zirconium in physical and mechanical properties, a number
of new deformation systems have been found [2, 4], which have not been observed in metals with a hexagonal
lattice. The occurrence of these deformation systems was also to be expected in zirconium.
Since attempts to obtain single crystal specimens by the strain-annealing method and by phase recrystalliza-
tion were unsuccessful, all the investigations were made on polycrystalline zirconium iodide.
The specimens 5 x 5 x 7 mm in size with a rather coarse grain (average diameter 0.5-1.5 mm) were ob-
tained by long annealing ( ? 10 hrs) at 830?C. Two specimens were studied. Two mutually perpendicular faces
on each of these specimens were ground and polished, and were etched in a 20% alcoholic solution of hydrofluoric
acid to reveal the grain boundaries. The coarsest grains were selected for investigation, these being situated near
the edge formed by the two polished surfaces and visible in both surfaces.
The orientation of the grains was determined by means of a special back-reflection camera using a primary
beam of a diameter not exceeding 0.2 mm. The camera was fitted with a microscope to enable the specimen to
be arranged so that the Laue pattern was obtained only from the grain, the orientationof which was to be deter-
mined. The distance from specimen to film was reduced to 16 mm in order to cut down the exposure time.
After the orientation of a number of grains had been determined, the specimens were deformed by upsetting,.
at room temperature,in a direction parallel to the edge formed by the two surfaces investigated.
The deformation lines on the surfaces of grains of known orientation were studied with the aid of an opti-
cal microscope and were photographed; The angle between these lines and the edge formed by the two surfaces
Investigated was measured on the. photomicrographs. The results were plotted on a Wulff-Bragg net and evaluated
in accordance with current technique [5].
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Determination of Twinning Systems
(1012) twins. The (1012) plane of twins of this type was identified by the two-surface method [5).
The results of the determination of the indices of this twinning plane and also of the other deformation
systems are shown on the standard crystallographic projection of the a-zirconium crystal (Fig. 1). The trace
of the same twin (1102) (Fig. 2) was discovered on both the grain surfaces investigated. The pole of the twinning
plane was determined in a well-defined manner as the position of intersection of the arcs of great circles perpen-
dicular to the corresponding traces of the twinning plane.
Fig. 1. Standardard polar diagram of a-zirconium on
which are marked portions of the great circle arcs
used for the determination of the indices of the K1
planes, twinning systems and the indices of slip planes.
) results of the determination of the indices by the
two-surface method.
Deformation Systems of Zirconium'
Twinning
Twinning
plane
Twinning
direction
Magnitude of
shear
ic1
K2
11
TI2
8 theor
sexp
(10I-2)
(1121)
(1122)
(1123)
(10-12-)
(0001)
?
?
110111M-ill
[1126J[1120]
[1123] ?
(1122J ?
I (1( 3___!.2..)
v5 c a?
a
?
c
?
?
0,173
0,629
--
--
Slip*
Slip plane
Slip direction
(101-o)
(1011)
[1210]
* Slip along the base plane was not observed.
Figure 1 also shows that in the region of the (1012) pole, a large number of arcs of great circles intersect
which are perpendicular to the traces of these (1012) twins, found on only one of the surfaces investigated, I. e.,
they were identified by the pole locus method [6]. (1012) twins are found in the majority of hexagonal metals
and have been well studied. The shear direction in twinning ni (1011] in the given case,is determined as the
position of intersection of the twinning plane and the plane of symmetry perpendicular to it. The twins often
have a lenticular shape and become thinner when they approach a grain boundary or another twin of this type
(Fig. 3).
The magnitude of the shear s was calculated from the measured values of the angles between the normals
to the polished surfaces and the normals to the surfaces of the twin lamellas (see for example (5)). The measure-
ment of these angles was made by means of an optical goniometer. The measured value of the angle 29 =
86.5 ? 1.5? corresponds to K2 (1012)and 772 [101.1]. The calculated value of the angle for this plane is 29 = 85?04'.
Twinning shear is comparatively slight (exp = 0.1'13), and therefore no exceptionally high stresses occur
In the matrix and the twins may be fairly wide.
The table shows the data characteristic of the (161.2) twins, as well as the formula for calculating the mag-
nitude of the shear, showing that the sign of the deformation (shear) depends to a considerable extent on the value
of the ratio c/a. If c/a < /3 (in the case of zirconium, c/a = 1.589), shear is in the [1011] direction, if c/a >
> /3 (in the case of zinc, c/a = 1.856), the direction of shear is reversed.
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Fig. 2. Mutually perpendicular surfaces of a-zirconium after deformation (x 100).
Fig. 3. Twins in a-zirconium (x 500).
(101) twins. Twins of the (11-21) type were like-
wise identified by the pole locus method and the two-
surface method (Figs. 1 and 2).
The direction of shear 712 [1126] in the present
case is also determined by the plane of symmetry of
the zirconium lattice. The magnitude of the shear was
determined in the same way as in the preceding case.
The measured value of the angle 29 = 73 t 1.5?, which
corresponds to 1 Eopt the cost increase becomes slower for larger values of S.
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It is also possible, in this way, to plot curves for operating power. In Fig. 12 is shown the dependence of
normalized operating power C/Wout on the electric field strength. These curves are similar to those shown in
Fig. 11. The minima of the power consumption curves lie in the region of small E0 and the consumption increases
sharply to the left of the minimum point.
The optimum values of the electric field corresponding to minimum operating costs are smaller than the
values of Eopt which determine the lowest constructional costs.
The curves in Figs. 11 and 12 indicate that the
power output of the rf generators used to supply power
to the accelerator section should be as high as possible.
C'10?
'you?
4
3
1
0
ev
5 -
30
5 '
S ,40
--
50
100
150
200
250 to,kv cm
Fig. 12. Normalized accelerator operation cost as a
function of field strength E0 for various values of the
rf power S (megawatts).
Thus, the cost of construction and operation of a
high-energy accelerator is characterized by minima
which correspond to definite values of the electric field
strength. These minima in the cost are independent of
electron energy at the accelerator output. ,
It follows that the optimum values of the basic
parameters for a high-energy linear electron accelerator
(field E0, rf power source, geometric dimensions of the
accelerating system and section length) are also inde-
pendent of the electron energy at the accelerator output.
In high energy accelerators the problems involved
in obtaining the highest possible current are of special
importance.
All other conditions remaining the same, the
average current in a linear accelerator is determined
by the length of the rf pulse. However, the pulses which can be obtained from presently available high-power
rf generators are of extremely short duration so that it becomes fruitful to investigate means by which these pulses
can be used more effectively in accelerating particles.
The electron acceleration actually takes place only during part of the rf pulse from the generator. This
useful part of the pulse is limited by the transient processes involved in establishing steady-state rf oscillations
in the accelerating system itself and in the feeder waveguides.
L
,Psec
gP
1,0
0,5
0 100 200 300
400
500 600 L ,m
Fig. 13. Reduction in the useful part of the rf pulse
due to the feeder line (rectangular waveguides) as a
function of accelerator length L. 1) Waveguide cross-
section '72 x 34 mm2; 2) waveguide cross section
110 x 54 mm2.
588
In systems in which the sections are supplied inde-
pendently this transient period is smaller than in other
types of systems.
The electron traversal time in a high-energy
linear accelerator is comparable with the duration of
the rf pulse obtained from the klystron generator in each
section. Thus, in order to obtain the most complete
utilization of these pulses for electron acceleration it
is necessary that the generators be switched on in a time
sequence rather than simultaneously. This situation can
be achieved if the signal which controls the application
of the high voltage to the klystron and the rf power from
a given generator are forced to propagate with the velo-
city of the electron being accelerated, that is to say,
with the velocity of light. This condition can be satis-
field without great difficulty in the first case; in the
second case, however, it poses a difficult problem. There
are two means by which this problem can be solved; in-
creasing the velocity of the electromagnetic waves in
the feeder waveguide and increasing the duration of the
pulse which excites the rf power.
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The velocity of propagation of the rf power in the waveguide is nothing more than the velocity of propaga-
tion of the pulse front, I. e., the signal group velocity vgp. It is determined by the type of waveguide which is
used. After the pulse front reaches a given point in the waveguide a transient process occurs and it is only after
a certain time interval At that the rf oscillations at a given point may be assumed to have reached steady-state
conditions. Calculations carried out by G. Ia. Liubarskii indicate that this time interval is small as compared
with the propagation time. Hence At will not be taken into account in the following. .
We now estimate the time required to achieve steady-state conditions in a system in which the accelerator
sections are supplied independently (cf. Fig. 2), assuming for simplicity that the time required to reach steady-
state conditions is equal to the propagation time. Using this procedure it is possible to determine the duration
of the useful part of the rf pulse; it is assumed that the electrons reach an accelerator section when steady-state
conditions have already been achieved.- The duration of the useful part of the pulse ro is given by the expression
[ (t -T) tIC+1Y+147
(9)
where r is the length of the rf pulse from the klystron, t = L/vgp is the propagation time for a pulse in a smooth
waveguide of length L, c is the velocity of light, tk is the time required for steady-state conditions to obtain in
the klystron, t is the propagation time for the rf oscillations in an accelerator section and td is the time spread
due to variations in the firing time of the trigger discharge gap.
The propagation for the rf pulse in the waveguide section Ty is determined by the decay factor a for the
accelerating field in the section. When a = 0.5, ty + tk 0.7 ?sec.
The reduction in the length of the useful part of the rf pulse due to the feeder line is L/vgp? L/c. The
magnitude of this difference is determined by the value of vgp in the feeder waveguide and is shown in Fig. 13
for, standard rectangulat waveguides.
A radical solution to the problem is the use of a coaxial waveguide (vgp = c) as the feeder line. In this
case the feeder line does not introduce any reduction in the length of the useful part of the rf pulse.
When a rectangular waveguide is used it is necessary to increase the duration of the rf pulse at the input to
the feeder line by an amount L/vgp? L/c. In this case, the high-voltage pulse at the accelerator klystron for
the first section must be delayed by an amount L/vgp ? L/c with respect to the triggering voltage pulse. A spe-
cial synchronization circuit must also provide appropriate time displacement in the application of the high-volt-
age to the other klystrons.
When above-indicated methods are used the useful part of the rf pulse is determined only by the time re-
quired to establish steady-state conditions in the accelerating section and the klystron, and the instability in the
firing time of the trigger discharge. The ratio of the useful part of the pulse to the total pulse is independent of
the final energy of the accelerated electrons.
LITERATURE CITED
[1] L. Levine, Contemporary Waveguide Theory [Russian translation] (IL, 1954).
[2] W. Walkinshaw, J. Appl. Phys. 20, 634 (1949).
Received May 14, 1957
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. Declassified and Approved For Release 2013/09/13: CIA-RDP10-02196R000100010004-9
SECONDARY NUCLEAR REACTIONS IN THE BOMBARDMENT OF
TIN BY FAST PROTONS
M. Ia. Kuzuetsova, V. N. Mekhedov, and V. A. Khalkin
A radiochemical method has been used to study the capture of pro-
ducts arising in disintegration of target nuclei.
Using the measurements of yields of radioactive isotopes of tellurium
(Z = 52) and iodine (Z = 53) obtained from tin (Z = 50) irradiated by pro-
tons with energy from 170 to 660 Mev excitation curves are plotted for the
secondary reactions which lead to the formation of products with charges 2
and 3 units greater than the charge of the original nucleus. The cross sec-
tions for these reactions increases with increasing energy of the incident
protons: a( a, x n) and a(Li, xn) are respectively 18.5 ? 5 and 0.17 ? 0.1
mbarns for E = 170 Mev and 50 ? 6.5 and 1.6 ? 0.5 mbarns for E = 660
Mev. The cross sections for lithium capture by tin in a comparable proton
energy interval are in good agreement with the results of investigations of
similar reactions in copper, tin and lead but are found to be 50 times smaller
than the cross sections obtained by Marquez and Perlman.
The observed cross sections for the secondary lithium capture can be
explained only by assuming that these nuclei acquire energies greater than
that which can be obtained in evaporation or fission of the target nuclei.
Secondary reactions of the (a, xn) type can be explained satisfac-
torily on the basis of an evaporation mechanism for the formation of the
helium nuclei.
When various elements are bombarded with protons with energies of several hundred million electron volts
one observes formation of radioactive nuclides with atomic numbers larger than that of the original nucleus
[1-6]. These nuclides are produced chiefly in capture of the disintegration products 2He4, 3Li and 4Be by the
target nuclei. The cross section for these secondary reactions is small. At energies of 340-480 Mev 0 Z +2
10-29 cm2 and 01+3 1031 cm2. In both cases the cross section increases noticeably with increasing energy.
For example, when copper is bombarded by 2.2 Bev protons the germanium formation cross section increases by
a factor of 10 as compared with the cross section obtained with 340 Mev protons.
The data obtained by different authors on the secondary-reaction cross sections are in satisfactory agree-
ment. The single exception is the work reported by Marquez and Perlman [2] in which the capture cross section
for lithium by tin is, in order of magnitude, almost equal to the cross section for the capture of a-particles, I. e.,
a factor of 50-100 greater than for other elements.
The present work has been undertaken for two reasons: firstly, to check the data obtained in [2] on the
cross section for the formation of iodine isotopes in the irradiation of tin and, secondly, to obtain additional data
required for an understanding cif the secondary-reaction mechanism.
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EXPERIMENTAL METHOD
Tin samples of high purity (impurity content less than 10-1 0/0) wrapped in aluminum foil were irradiated
by protons at different radii in the synchrocyclotron chamber. The target weights were 0.2-0.5 g. The irradia-
tion lasted for 1-2 his. The intensity of the proton beam was determined from the Na 24 accumulation in an alu-
minum monitor. In the proton energy region which was investigated the cross section for the A121(p, 3pn)Na24
reaction was taken as 10 mbarns.
Iodine extraction. After irradiation the samples were dissolved in fuming concentrated nitric acid, con-
taining calcium persulfate, 30 mg of iodine (KI03) and 50 mg of tellurium(nitric acid solution). The solution,
was diluted to 80-100 ml and the iodate was reduced to the iodide by sodium sulfate. The iodine was distilled
successively through two absorbers. The first absorber was filled with a 1 M solution of HNO3 and the second with
a 1 M solution of NaOH. Then the elementary iodine was extracted twice with chloroform.
In the measurements a target of PdI2 was used. As a rule the chemical yield of the carrier was 60-70%.
A special check showed no loss of radioactive iodine due to absorption in tin dioxide formed when the metallic
tin was dissolved in the HNO3,
Tellurium ext/action. When the iodine extraction was completed contents of the distillation flask were
evaporated and the residue of tin dioxide was dissolved in concentrated hydrochloric acid. After removal of the
excess HNO3 the tellurium was precipitated by tin dichloride. The residue Was centrifuged and again dissolved
in a mixture of hydrochloric acid and nitric acid. 1-2 mg of the reverse carriers were added to the solution:
selenium, antimony, arsenic, copper, etc. and it was evaporated until practically dry. The selenium, antimony,
gold, and arsenic were separated by double evaporation of a solution with three ml of HBr. All traces of the HNO3
were removed simultaneously. The residue was dissolved in a 3 M solution of HCI and the tellurium was precipi-
tated from the boiling solution by sulfur gas. The evaporation of the HBr solution and the precipitation of metallic
tellurium by sulfur gas were carried out twice. In order to keep the tellurium pure from contamination by precious
metals it was distilled in a hydrogen stream at a temperature of 800-900?C. The condensate was washed in nitric
acid and evaporated with HC1 and HBr. The metallic tellurium precipitated by the sulfur gas was deposited on
the target. The chemical yield was 20-400/0.
Radioactivity measurements. The measurements of sample activity were carried out with an end counter
with a mica window approximately 3 mg/cm2 thick. The following iodine isotopes were found: 1126 (8 , K, T =
= 13 days); 1124 (8, K, T = 4.5 days); 1123 (K, T = 13 las); 1121 (8 , K, T = 1.8 his); 1120 (8
= 30 min). The
K-capture fractions in 1126, II2A and '121, according to our measurements, which will be published, were 50, approxi-
mately 60 and approximately 6010, respectively. One half-life of approximately six days was found in tellurium.
This activity was assigned to Te112 (K, T = 6 days), which was detected by means of the daughter nuclei Sblig
, T = 3.5 min, E8 = 3.1 Mev). It was impossible to distinguish periods corresponding to Te 112 (K, T = 4.5 days),
on the decay curve because of the proximity of the half-lives for Te 112 and Tells and the low efficiency for x-rays.
A 2.5 hr activity (Tel") was not observed.
EXPERIMENTAL RESULTS
The identification of the reaction products with charges 2 and 3 units greater than that of the original
nucleus and the production cross sections for the products at various proton energies are shown in Table 1. In
this table are shown the arithmetical averages of the experimental deviations for the cross sections as determined
from three papers.
The low radioactivity of the targets and the large number of iodine isotopes complicated the resolution of
the decay curve and the determination of the yields for individual products. The formation cross section for 1121
may be taken as completely reliable. The total cross section may be somewhat high because of internal-conver-
sion electrons in I. * It would seem that the absolute uncertainty in the total cross section is small since the
? In determining the 1123 production cross section internal-conversion electrons were taken into account. The
efficiency for x-ray detection of the end counter found with a standard Ins sample (K. T = 60 days) was 20/0. Sup-
plementary measurement with a cylindrical counter with aluminum walls verified the analysis of the decay curves.
In this case 1123 was not detected but the yield of the other isotopes were found in agreement with the data ob-
tained with the end counter.
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TABLE 1
Cross Sections for the Production of Isotopes of Tellurium and Iodine in the Bombardment of Tin by Protons of
Various Energies (mbarns)
Isotope
Half-life
Data of present work
Data of 161
170 Mev
340 MeV
480 MeV
660 Mev
340 Mev
480 Mev
Teto
pail
I121
J183
1124
1126
Total cross
iodine isotope
6 days
30 mm
1,8 hrs
13 hrs
4,5 days
13 days
section for
3,6 ?1,0 16,5 ?1,5
0,02+0,01 0,03+0,01
0,02?0,0050,067?0,003
0,11+0,08 0,3+0,07
?0,01 0,024
?0,01 '0,02
0,17+0,1 0,44+0,084
14,5 ?7,7
0,10+0,01
0,15+0,03
0,56+0,16
0,035
0,048+0,006
0,9 +0,2
10 ?1,3
0,27+0,2
0,24+0,007
0,97+0,2
0,06+0,008
0,06+0,01
1,6 ?0,5
5,0
0,05
0,17
0,18
} 0,11
0,51
11
?
0,45
0,38
0,41
1,24
20
Tellurium 7
r1I The possibility that the cross section measured
in the present work was too low because of iodine loss
Astatine 100
in the target due to heating in the vacuum chamber of
zr
80 I the synchrocyclotron during the bombardment was ex-
eluded by control experiments. In these experiments
Iodine 60 the bombardment was carried out on tin samples sealed
40 in a thin-walled glass ampule. The cross sections for
200 the production of iodine isotopes obtained in this case
were in agreement with the cross sections shown in Table 1.
Yields of iodine and tellurium from tin for protons of An analysis of possible contaminants indicates that any
contribution due to impurities in the formation of active
iodine is negligible. Thus, the separation of barium
(Z = 56) showed that any contribution to disintegration of impurities could be responsible for only 1/25 of the
active iodine.
The variation in the iodine production cross section with increasing proton energy is shown on the lower
curve in the figure. The steeper increase in the cross section in the proton energy region above 400 Mev is due
primarily to the increased yield of light iodine isotopes and can be explained by the formation of these isotopes
in capture of fast protons with subsequent emission of two w-mesons and several neutrons. Unfortunately, the
scarcity of experimental data makes it impossible to estimate the contribution arising from these reactions and
to delineate the energy region in which they occur.
Only the a-production cross section was determined from the cross sections for secondary capture of Tells
particles (cf. Table 1). It reaches a maximum value at a proton energy line between 340-500 Mev and then
falls off (cf. figure). A similar pattern is observed for the formation of light isotopes of astatine from bismuth
results of [6] (Table 1), obtained by a somewhat dif-
ferent method, are in rather good Agreement with the
present data. Moreover, the cross sections which have
been found are approximately the same as the cross sec-
tions for the production of germanium isotopes and At211
in bombardment of copper and lead by protons [3](cf.
Table 2). Thus, it follows from the present data that
the cross section for the secondary reaction involving
lithium capture by tin at proton energies of 340 Mev is
50 times smaller than the values obtained by Marquez
and Perlman [2]. In the present work the same iodine
isotopes were found but the relative yields were very
much different from the data reported in [2].
400 600
800
MeV
various energies.
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Ell and Ga66 from copper [5]. The peculiar dependence may best be explained by the existence of supplementary
Tel production reactions due to fast protron capture by target nuclei with the subsequent emission of tr"-mesons
and several neutrons. It is more difficult to explain the effect on the curve of changes in the spectrum and the
probability for a-particle production because there is no explanation for the drop in the curve in the high-energy
region.
TABLE 2
Cross Sections for Secondary Capture of a-Particle and Lithium Nuclei for Copper, Tin, Bismuth.and Lead
Reaction
Original
element ,
Reaction product
Experimental
cross section
10-3? cm2
Extrapolated
cross section
-.10
10 cm2
Literature
reference
a- Particle
capture
Cu
Sn
Ga60--FGa67-1-Ga68
Tem
26 (346)
8 (480)
90
40
[31
Present
work
Bi
At210+At211
80(480)
80
[1]
Cu
Ge66-FGen+Gee9
0,3 (340)
0,6
[3]
Lithium
capture
Sn
Iiso+1121+1123+11.24+pss
0,9(480)
0,9
Present
work
Pb
Atm
0,04-0,08
0,16-0,32
[1]
It is possible to estimate the contribution of the (a, xn) reaction in the production of Tell? in the region
180-660 Mev if it is assumed that: 1) at proton energies of 180 and 660 Mev the Tell? is produced basically
through this reaction and 2) in this energy region the Tel production cross section in the (a, xn) reaction
changes in linear fashion (dashed line on the figure). The integrated energy dependence for the total cross sec-
tion for the (a,xn) reaction in tin is found to be approximately the same as the dependence of the astatine pro-
duction cross section in bismuth bombardment (solid line in the figure). The last fact may be considered veri-
fication of the present interpretation. At proton energies of 480 Mev the integrated value of the Tell? produc-
tion cross section in the (a, xn) reaction is 8 mbarns.
DISCUSSION OF RESULTS
In comparing the present data with data reported by other authors [1, 3] it is necessary to estimate the
total tellurium production cross section. For this purpose it is sufficient to multiply the Te ll? production cross
section by a factor of approximately 5.* The total tellurium production cross section determined in this way
(40 mbarns at E = 480 Mev) is found to be approximately the same as the cross section for the formation of
gallium isotopes from copper [3] and At21? and At from bismuth [1] in a comparable incident-particle energy
range (Table 2).
It is interesting to compare the presently available data on secondary-reaction cross sections. These data are
shown in Table 2. In this table are shown the experimental cross sections obtained at various proton energies
(the energy values in Mev are shown in brackets). In a number of cases not all the reaction products are observed.
Hence, in order to make a comparison it is necessary to extrapolate the cross sections at the same energy of the
bombarding particles and to take account of the unobserved reaction products. The extrapolated cross sections
for E = 480 Mev are shown in the next to the last column in Table 2. In extrapolating the cross sections it has
been assumed that the energy dependence of the secondary-reaction product yields in copper is similar to those
in tin and bismuth. Correction factors which take account of the increase in cross section as the energy is Changed
from 340 to 480 Mev were found to be 1.0 for gallium isotopes and 2.0 for germanium. The correction factor for
? In studying the production of astatine from bismuth [1] it was found that the astatine is formed mainly as a
result of (a, 2n) and (a, 3n) reactions. Assuming a similar mechanism for Tell? production and taking account
of the abundances of the tin isotopes Sn1l6 and slim (200/0) we obtain the factor of 5 indicated above.
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the unobserved products of a-particle capture in the copper case was approximately 3 (the isotopes Ga, Ga67
and Ga68 obtained mainly from the (a, 2n) and (a, 3n) reactions in the Cu65 isotope, characterized by an abun-
dance of 30%. For tin this factor is 5 as indicated above. In determining the total cross section for the produc-
tion of astatine from lead the Atm production cross section was multiplied by a factor of 4. However, the extra-
polated cross sections for astatine is too low as a consequency of the incomplete chemical separation of At2I1 in
It is apparent from Table 2 that the a-particle capture reaction is characterized by approximately the
same cross section in nuclei with entirely different atomic numbers.
The reaction cross section for lithium capture is approximately two orders of magnitude lower than the
cross section for a-particle capture and is also essentially independent of the atomic number of the.bombarded
elements.
The last finding is somewhat unexpected. In the literature it is reported that the yields of the light nuclei
Lis and Be7 are reduced noticeably with increasing Z of the target nucleus [2, 7]. Hence, the cross section for
secondary capture of lithium should be reduced by approximately a factor of 10 in going from copper to lead.
If the observed cross section for the capture of a-particles can be explained satisfactorily by assuming
that these particles are formed in an evaporation process, the interpretation of the lithium reaction requires other
assumptions. In analyzing the yield of iodine from tin, Marquez and Perlman [2] assume that all the lithium
nuclei are emitted with energies of 80 Mev. However, their calculations lead to computed production cross sec-
tions for Lis or Be7 which are 500 times higher than the experimental cross sections.
A calculation based on tbe Marquez and Perlman scheme, using the iodine yield obtained in the present
experiments with Ep = 340 Mev, gives a value of approximately 0.5 mbarns for the lithium production cross sec-
tion. This quantity is approximately ten times larger than the Lis production cross section in xenon [7] or Be7 in
silver [2] in bombardment by protons of approximately the same energy. However, this discrepancy is not of great
importance in view of the qualitative nature of the estimate and the fact that lithium isotopes other than Lis can
take part in the secondary reactions. The cross section for the production of lithium nuclei with energiei higher
than Coulomb barrier can be estimated from the result of a study of stars from fragments in photoemulsions. Such
fragment observations (Z 4) have been carried out at the synchrocyclotron by Lozhkin and Perfilov [8]. An
analysis of the results of this work shows that the cross section for the formation of lithium is 0.1 mbarns, a value
which is in rather good agreement with the present computed value.
A calculation carried out under the assumption that all the lithium nuclei are formed with energies of 40
Mev yields a value which is approximately 15 times greater than the value of the cross section obtained from a
calculation in which it is assumed that the nuclei have energies of 80 Mev.
Using the iodine isotope yield an attempt was made to approximate the energy spectrum f (E) of the emitted
lithium nuclei. The estimate was made on the basis of the expression*
co
B n I (E)dE (E) dE
dE
0 Ho dx
and indicates that the assumption of a steeply dropping spectrum leads to a value of the lithium production cross
section which is much too high. Thus, for a spectrum extending to 80 Mev following a 1/E2 relation the value
aLt = 1 mbarn is obtained. For a 1/E8 spectrum the quantity ou is found to be approximately 20 mbarns, i. e.,
considerably larger than the experimentally observed cross section for the formation of Lis for Be7. The basic
error in these estimates arises as a result of the uncertainty in the excitation function for the (Li, xn) reactions;
-these are approximated by analogy with the excitation function for (a, xn) reactions.
dE
? In this expression; B is the capture product yield, n is the number of tin nuclei in 1 ems; ? ? is the
dx
energy loss of the lithium nuclei in ionization, ,E0 is the initial energy in the excitation function for the capture
of lithium by tin a(E).
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Because of the qualitative nature of the calculations it is impossible to draw any definite conclusions as to
the energy spectrum of the reacting nuclei. However, these estimates do indicate that if one is to explain the
the observed cross section for secondary capture of lithium nuclei it is necessary to assume that these nuclei are
formed with energies considerably greater than those which would be obtained in evaporation or fission of the
original target nuclei. It is reasonable to suppose that the emission of fast fragments, which are responsible for
the secondary reactions, occurs in the collision of the incident protons with the substructure of the nucleus which
is formed as a result of fluctuations in the density of nuclear matter. Such ideas have already been proposed
several times in the literature 18, 9] but no final theory for this effect has as yet been suggested. We propose
that, along with other methods of investigition, a successful understanding of the features of this interaction me-
chanism will be achieved by further study of secondary reactions.
.The authors are indebted to B. V. Kurchatov, V. G. Solov'ev, and I. Iu. Levenberg for help in carrying out
the present work and to V. P. Dzhelepov, M. G. Meshcheriakov and G. A. Leskin for a number of valuable critical
remarks.
LITERATURE CITED
[1] B. V. Kurchatov, V. N. Mekhedov, M. Ia. Kuznetsova, L. I. Kurchatova and N. I. Borisova, Combined
Report of the Joint Institute for Nuclear Research No. 633 (1951).
[2] L. Marquez and I. Perlman, Phys. Rev. 81, 953 (1951).
[3] R. E. Batrel, D. K. Miller and L. T. Seaborg, Phys. Rev. 84. 671 (1951).
[4] A. Tarnevich and N. Sugarman, Phys. Rev. 94, 728 (1954).
[5] A. P. Vinogradov, I. L. Alimarin, V. I. Baranov, A. N. Lavrukhina and F. I. Pavoltskaia, Conference
of the Academy of Sciences USSR on the Peaceful Use of Atomic Energy (Division of Chemical Sciences) Izv.
Akad. Nauk SSSR 1955, p. 97.
[6] B. V. Kurchatov, V. N. Mekhedov, L. I. Kurchatova, M. Ia. Kuznetsova and L. V. Kuznetsova, Com-
bined Report for the Joint Institute of Nuclear Research No. 258 (1953).
[7] S. C. Wright, Phys. Rev. 79, 838 (1950).
[8] 0. V. Lozhkin and N. A. Perfilov, J. Exptl. Theoret. Phys. (USSR) 31. 913 (1956),
[9] D. I. Bloc Blokhintsev, Usp. Fiz. Nauk 61, 137 (1957).
Received June 18, 1957
? See English translation.
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DOSE CHARACTERISTICS OF A MIXTURE OF URANIUM FISSION FRAGMENTS
K. K. Aglintsev, A. N. Gorobets, V. P. Kasatkin, and E. S. Kondakova
Results are presented for calculations for the different dose charac-
teristics of fragment elements: the percentage composition of the mix-
ture for a uranium exposure time to = 100 days and a cooling off period
r = 15540 days, the time variation of the activity of the mixture for to,
equal to 60, 100 and 150 days. The calculated data are in satisfactory
agreement with the results of radiochemical analyses.
The gamma constant of the mixture is essentially independent of
to (within the limits 60-150 days) and also remains approximately con-
stant for values of r ranging from 15-180 days.
The operation of nuclear reactors results in the formations of appreciable numbers of radioactive fragment
nuclides. The practical utilization of preparations made from a mixture of fission fragments requires a knowledge
of the radiochemical composition and dose characteristics of these mixtures. Obviously, special attention is meri-
ted by those nuclides which are characterized by relatively high yields and long half-lives and the two-, or three-
member chains which contain such nuclides. Data on these nuclides are given in Table 1 [1-4]. In those cases
in which the nuclide is not produced directly in uranium
TABLE 1 fission but results from the decay of the fragment nuclei
the table indicates the chain which leads to the forma-
Yields and Decay Chains for Certain Fission Fragments
tion of this nuclei.. No gaseous fission fragments (kryp-
Nuclide
Fission -
yield, To
Chain
Sr 89
4,8
Se?
5,8
_
Srol
5,1
_
y9O
?
Sr"---Y90
yin
5,9
?
yin
?
Sr91-->Y91
Zr95
6,0
_
Nb95
?
Zr95-->Nb95
Rum
2,9
_
Ruios
0,4
_
Rho?
?
Ruioe__>Rh1013
'
Cs'"
5,9
_
Bahl?
6,3
_
Be"
4,6
_
Lau?
?
Ba14??>La149
Leda
3,8
?
ceui
5,7
?
Ceul
?
Bau1?>La141?>Cel4i
C043
5,4
_
Ce144
6,2
?
Pr143
?
La159-->C043--->pr143
Pe"
?
Ce144?>Pr144
Nd147
2,6
_
pm147
2,6
_
Nabs?
?
Nd147?Pm1147
ton, iodine, xenon) are shown in Table 1 since these
escape from the fragment mixture.
A calculation of the activity of nuclides formed
directly in fission or in two-member chains leads to the
expressions:
007 at = Fp,(1 ? e?Aito) e?xr: ,
F
(X 2 ? _ ,
N 2Y : ?
, F piT2
-t- 7 ?, (1 e?x2to) e?A2T.
?/
where pi is the fission yield, to is the length of time the
uranium is exposed in the reactor, r is the time reckoned
from the termination of exposure, x1, X2. T1 and T2 are
the decay constants and the half-lives of the nuclides,
and F is the number of fission events per kilowatt of
reactor power.
In Fig. 1 are shown the results of the calculation
of the percentage radiochemical content of uranium
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30 -
20
10 -
8 ---
7 -
6 ---
5
4
3 -
-
2 -
1,0
0,5
115 20
111111
30 40 50 60 80 100
I 1 I I
I
150 200 300 400 500 600
2, days
Fig. 1. Radiochemical composition of a mixture of uranium fission fragments of
different age (to = 100 days). The Pr144 and Y9? content are determined from the
curve for Ce144 and Sr".
TABLE 2
Percentage Content of Isotopes for Various Cooling-
Off Times for Fission Fragments to = 100 days
Nuclides
To content
1=45 days
To content
T=400 days
calc.
exptl
calc
exptl
Sr89+Sroo
ygo+ysi
Zr95
ram
Ruin
Rhios
CO"
Bed?
Lau?
Ce141+Ce14?
pr143
pr144
pm147
Lauo+Pri43+Pm147
cei41+ce144+pr144
11,2
14,1
14,2
15,9
8,3
-
-
3,4
4,0
17,0
3,7
6,5
1,2
8,9
23,5
11,4
17,7
13,6
12,8
5,1
-
-
3,9
-
-
-
-
-
9,2
24,2
,4,3
5,3
4,2
8,5
-
2,7
2,6
-
-
30,2
-
30,2
10,2
-
60,4
7,2
5,0
3,2
4,6
-
1,0
2,9
-
-
33,0
--
33,0
11,5
-
66,0
598
fission fragments for to = 100 days and r = 15-540
days. In Fig. 2 is shown the time variation of the total
activity, A, of fission fragments for to equal to 60, 100
and 150 days.
Table 2 contains a comparison of the calculated
data and the results of radiochemical analyses of a mix-
ture 'of uranium fission fragments for to equal to 100
days and r equal to 45 and 400 days.
It is apparent from Table 2 that the experimental
and calculated data are in satisfactory agreement.
The dose characteristics of a mixture of fission
fragments are determined by the energy distribution of
the electron in the a - s p ec tr um of the mixture, the
energy of the y -rays and the number of y -photons per
8 -particle. The data on the B -spectrum determine the
penetrating power and the surface and depth doses in the
field of a radiator for any configuration; the data on
the y -spectrum determines the y -constant and the pene-
tration power of the y -radiation.
The B -spectrum of a mixture of fission fragments
is extremely complicated; in a mixture of fission frag-
ments one encounters a -spectrum with maximum ener-
gies ranging from 0.16 Mev (Nb95) to 3.5 Mev (the partial
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A, curies/kw
1000
500
200
100
50
20
10
5
2
10
20 40 60 100 200 400
to-150 day
to-700day
to-60 day
600 1000
days
Fig. 2. Time variation of the total activity of a mixture of uranium fission fragments.
8 -spectrum of Rhu6). The relations between the soft and hard 8 -spectrum change continuously in accordance
with the composition of the mixture of fission fragments.
The main y -radiators in a mixture of fission fragments are: Zr95, Nb95, Rum, Rh166, Cs137, Baia, Lam,
Pr144, Nen. The remaining nuclides are either very soft (h v < 200 key) or very weak y -radiators.
In a fresh mixture (7- 60 days) the most important y -radiators are; Ball?. Lau% Zr, Nb" and Nd147;
in a medium age mixture (60 360 days) the important radiators are Cs137,
Rh106. pr144.
The y -corstant of the mixture, i. e., the dose in r/hr at a distance of 1 m from a preparation of 1 curie
strength is obtained by summing the values of the y -constants of the individual nuclides multiplied by their frac-
tional content in the mixture. The results are shown in Table 3.
As is apparent from Table 3 the y -constant remains approximately constant within the limits 0.15-0.17
r/hr-curie-meter for a mixture of age r = 15-180 days, and then falls off rapidly to 0.07-0.08 r/hr-curie-meter
for T = 360 days and finally to 0.02 r/hr-curie-meter for an age of 540 days.
This dependence Of the y -constant on the age of the fission fragments is due to the fact that at ages greater
than 180 days the amount of Zr 95 + Nb95 falls off rapidly and is not compensated by the slow increase in the long-
lived nuclides Cs irr and Rh106.
TABLE 3
Values of the y -Constant for a Fragment Mixture as a Function of T and to
to
15
.30
45
60
90
120
150
180
360
540
,
60
0,175
0,160
0,150
0,152
0,155
0,155
0,155
0,155
0,080
0,020
100
0,175
0,170
0,150
0,155
0,155
0,155?
0,150
0,140
0,070
0,020
150
0,170
0,160
0,165
0,155
0,155
0,155
0,150
0,140
0,065
0,020
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R, g"equiv Ra/kw
100
50
to-150 days
to-100 da
t0=60 iai.S
20
10
5
2
0,5
0,2
0,1
10
20 40 400 600
days
Fig. 3. Time variation of a y -equivalent of a mixture of uranium fission
fragments.
60 100
200
The conversion from the values of the y -constant in r/hr-curie-meter to the y -equivalent preparation in
g-equivalents of radium is carried out by dividing by the factor 0.84. Values of the y -constant 0.02, 0.07, and
0.15-0.17 - r/hr-curie-meter correspond to values of the y -equivalent of 0.024, 0.096 and 0.18-0.20 g-equiv.
Ra /curie.
An examination of Table 3 indicates that the basic dose characteristics of a mixture of fission fragments ?
the y -constant for the number of g-equivalents of radium per curie is essentially independent of to the duration
of the uranium exposure in the reactor when to lies between 60 and 150 days. Precisely the same change in the
7-constant with age r of the mixture is found for different values of to. From Fig. 2 it is also apparent that when
to is increased the activity of the mixture increases; this situation is especially noticeable at high values of r.
Comparing the data in Fig. 2 and Table 3 it is easy to find the y -equivalent R of a fragment mixture, expressed
In g-equivalents of radium per kilowatt of reactor power. These values are shown in Fig. 3.
LITERATURE CITED
[1] C. Coryell and N. Sugermann, Radiochemical Studies. The Fission Products (McGraw-Hill, N. Y. 1951).
[2] G. Reed and A. Turkevich, Phys. Rev. 92, 1473 (1953).
[3] L. Glendenin et al., Proc. Intern. Conf. Peaceful Uses of Atomic Energy, Geneva, 1955 (N. Y., 1956),
vol. '/, p. 3.
[4] W. Hardwick, Phys. Rev. 92, 1072 (1953).
Received September 5, 1957
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2t
LETTERS TO THE EDITOR
BREMSSTRAHLUNG IN NUCLEAR FISSIONS
A. I. Alekseev
The Coulomb interaction between nuclear fragments leads to electromagnetic radiation in the decay of
nuclei. The calculation of this radiation can be simplified considerably if account is taken of the following.
The electromagnetic radiation is most intense while the fragments move in a region with dimensions of the order
of the Bohr radius of the mother atom; in this region the moving fragments have not yet been"covereeby the
electrons and thus the Coulomb interaction is strongest. The probability that the nuclear fragments will attract
electrons of the mother atom is very high [1] since in all cases of nuclear decay the fragment velocity is no
greater than the mean velocity of the electrons in the atom. If the fragment velocity is much smaller than the
mean velocity of electrons in the outer shell of the mother atom the ionic charge of decay products is essentially
zero at the beginning of the trajectory [1], 1. e., there is almost complete shielding of the fragments by the elec-
trons of the mother atom. In what follows we shall be interested only in the continuous bremsstrahlung of the
fragment and shall neglect the radiation associated with individual photons due to changes of the electronic shells
in covering the fragments. A consideration of the mass defects of nuclei shows that in heavy nuclei energies
ranging from several million electron volts to 200 Mev are liberated in a single fission event [2]. At these ener-
gies the de Broglie wavelength of each fragment is much smaller than the dimensions of the region of intense
radiation. Thus, in the decay of a nucleus with charge Z into two fragments with mass numbers A1 and A2 we
find
1.1.= e2 Z (Te., )1/2 ( mec2 )1/2
a he 1/.7t
2?s
(1)
where Xs is the de Broglie wavelength of the s th fragment (s = 1.2); a is the Bohr radius of the mother atom;
m and me are the masses of the nucleon and electron, respectively; Es is the kinetic energy of the sth fragment
after fission; e2/Hc = 9131. In decay of heavy nuclei the energy Es is usually reckoned in the order of millions
of electron volts so that in fission the ratio Xs/a is smaller than 10-2. As is well known, the fact that the de
Broglie wavelength is small compared with the characteristic dimensions of a charge means that a classical de-
scription can be used in analyzing the motion of the particle . Hence, we can use classical considerations to
compute the electromagnetic radiation characteristic of the flight of fragments from the point at which they
escape through the potential barrier out to infinity. This analysis, however, is not applicable in the small region
close to the point at which the fragments pass through the potential barrier (i. e., the point at which the classical
momentum of the fragment is zero); in this region the basic requirement for applying a classical description is
not satisfied [3]:
(2)
where p(r)?m=.. 12?(E? U(r)) is the classical momentum of a particle of mass ? moving with a total energy E in
a potential U(r). Estimates show that the region of values of r in which the requirement in (2) is not satisfied
is of the order Ar = 10-2 R (R is the point at which the fragment escapes from the potential barrier, being deter-
mined by the equation E? U(r) = 0), so that the fragment radiation in this region is small as compared with the
total bremsstrahlung.
? The present report is part of a diplomate thesis carried out by the author in 1952 at MIFI under the direction
of A. B. Migdal.
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We consider the decay of a nucleus into two fragments with mass numbers A1 and A2 and charges Zi and
12. In moving in a region with dimensions of order a the fragments interact in accordance with Coulomb's law;
outside this region the fragments are covered by electrons so that the interaction is described by a more compli-
cated relation. However, an estimate indicates that the bremsstrahlung outside the region of order a is (R/a)s
times smaller than the bremsstrahlung inside this region. We can thus neglect completely the bremsstrahlung
outside the region a. It is sufficient to consider the fragment motion inside this region. Because of the Coulomb
interaction the fragments are accelerated. In accordance with the laws of classical electrodynamics a charge
which moves with accelerated motion must radiate. Under these conditions the time for intense fragment radia-
tion is a/v (y. is the mean relative velocity of the fragment), so that the energy is radiated mainly as a wave of
frequency co which is smaller than v/a:
(0