THE SOVIET JOURNAL OF ATOMIC ENERGY VOLUME 10, NO. 3

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• Document Creation Date: December 23, 2016
• Document Release Date: March 1, 2013
• Sequence Number: 2
• Publication Date: January 1, 1962
• Content Type: REPORT

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Volume '10, No. 3
January, 1962
THE SOVIET JOURNAL OF
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU
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Research by Soviet Experts
Translated by Western Scientists
Soviet Research on the LANTHANIDE
AND ACTINIDE. ELEMENTS, 1949-1957
An important contribution to the literature of nuclear chemistry, this collection of papers is a
comprehensive presentation of Soviet research on the chemistry of lanthanides and actinides. The 106 reports
included inhis collection appeared in the major. Soviet chemical journals translated by Consultants 'Bureau,
as we*-as'in_the Soviet Journal of Atomic Energy, 1949-1957.
The five sections, totalling 657 pages, provide broad representation of contemporary Soviet
research in this important aspect of nuclear science. This collection should be accessible to all nuclear
researchers, whether theoretical or applied.
Each part may be purchased as follows:
Basic Chemistry (25 papers) ..................................$15.00
Analytical and Separation Chemistry (30 papers)............$20.00
Nuclear Chemistry (and Nuclear Properties) (32 papers) :..$22.50
Geology (10 papers) ........................... :............... $7.50
Nuclear Fuel Technology (9' papers) . ... ..................... $7.50
`Complete collection .......................................... $65.00
RADIATION CHEMISTRY,
PROCEEDINGS OF THE FIRST
ALL-UNION CONFERENCE MOSCOW,- 1957
More than 700 of the "Soviet Union's'-outstanding research scientists participated in this
conference sponsored by the Academy.of Sciences and the Ministry of the Chemical Industry. Each of the
.56 reports read in the various sessions covers either the theoretical or practical aspects of radiation chemistry,
and special attention is given to radiation sources used in -radiation-chemical investigations. The general
,discussions which followed each report and reflected various points of view on the problem under analysis
are also included.
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Primary, Acts in Radiation Chemical Processes
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Radiation Chemistry of Aqueous Solutions (Inorganic and Organic Systems)
heavy paper covers 15 reports, plus discussion ...... illustrated .......... $50.00
Radiation Electrochemical Processes
heavy paper covers 9 reports, plus discussion ...... illustrated ......... $15.00
The Effect of Radiation on Materials Involved in Biochemical Processes
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Radiation Chemistry of Simple Organic Systems
heavy paper covers 9 reports, plus' discussion ...... illustrated ......... $30.00
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EDITORIAL BOARD OF
ATOMNAYA ENERGIYA
A. I. Alikhanov
A. A. Bochvar
N. A. Dollezhal'
D. V. Efiremov
V. S. Emel'yanov
V. S. Fursov
V. F. Kalinin
A K Krasin
A. . V. . Lebedinskii
A. I. Leipunskii
I. I. Novikov
(Editor-in-Chief)
B. V. Semenov
V. I. Veksler
A. P. Vinogradov
N. A. Vlasov
(Assistant Editor)
A. P. Zefirov
THE SOVIET JOURNAL OF
ATOMIC ENERGY
A translation of ATOMNAYA ENERGIYA,
a publication of the Academy of Sciences of the USSR
(Russian original dated March, 1961)
vol. 10, No. 3
CONTENTS
January, 1962
RUSS.
PAGE PAGE
f The Livermore Variable-Energy 230 cm Cyclotron. H. Hernandez, J. Peterson, B. Smith,
and C. Taylor. Nuclear Instruments and Methods 9, 287-302 (1960); North Holland
Publishing Co. Also UCRL Report No. 5971, Reprint No. 1961-106 ......... , . 205]
The Selection of the Optimum Parameters for an Atomic Electric Generating Station.
A. Ya. Kramerov ............................................ 201 211
Corrosion Resistance of Steels and Zirconium Alloys in Boric Acid Solutions at Different
Temperatures. M. A. Tolstaya, S. V. Bogatyreva, and G. N. Gradusov .......... 213 222
On the Character of Residual Defects in Deformed and Neutron-Irradiated Monocrystals.
E. V. Kolontsova ......... .................................. 218 227
The Separation of Radium from Impurities by Means of Ammonium Carbonate. N. P.
Galkin, A. A. Maiorov, G. A. Polonnikova, V. G. Shcherbakova, and L. V. Utkina... 223 233
The Effect of Radioactivity of Substances on Their Physicochemical Properties. L. M.
Kopytin and Yu. V. Gagarinskii ..... ....................... ... 228 238
Application of Stable Boron Isotopes. S. P. Potapov .......................... 234 244
Investigations of the Radiation Purity of Atmospheric Air and of the River Neva in the
Region of Berth Tests of the Atomic Icebreaker Lenin. Yu. V. Sivintseva, V. A.
Knizhnikov, E. L. Telushkina, and A. D. Turkin ......................... 242 253
Production of Monoenergetic Beams of Accelerated Particles. F. R. Arutyunyan and
I. P. Karabekov ............................................. 248 259
Cross Section of the (d,p) Reaction on Various Nuclei. M. Z. Maksimov ............. 250 260
Theory of the Effective Cross Sections of Heavy Nuclei in the Region of Partial Neutron
Resonance Overlapping. A. A. Luk'yanov and V. V. Orlov .................. 252 262
Fast Neutron Capture Cross Sections for Niobium, Nickel, and Iron. Yu. Ya. Stavisskii and
A. V. Shapar' . ............................................... 255 264
Some Remarks Concerning the Determination of the Photoneutron Yield of Thick Specimens.
V. I. Gomonai, D. I. Sikora, and V. A. Shkoda-Ul'yanov ................... 257 265
Calculation of Mutual Shielding of Lumps in a Tight Lattice. N. I. Laletin ............ 258 267
Effectiveness of a System of Absorbing Elements Symmetrically Arranged in a Ring in the
Active Zone of a Reactor with Reflector. V. I. Nosov ..................... 262 269
On the Approximate Solution of the Transport Equation by the Method of Moments. Sh. S.
Nikolaishvili ............................................... 263 271
The Growth of Vapor Bubbles Moving In a Volume-Heated Fluid. V. K. Zavoiskii ...... 266 272
On the Theory of Hasiguti, Sakairi and Sugai Concerning the Irradiation-Induced Growth
of a-Uranium. Yu. N. Sokurskii................................... 269 274
Annual subscription $ 75.00
? 1962 Consultants Bureau Enterprises, Inc., 227 West 17th St., New York 11, N. Y.
Single issue
20.00
Note: The sale of photostatic copies of any portion of this copyright translation is expressly
Single article
12.50
prohibited by the copyright owners.
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CONTENTS (continued)
RUSS.
PAGE PAGE
Phase Composition in Nickel-Rich Alloys of a Nickel-Molybdenum-Boron System. P. T.
Kolomytsev and N. V. Moskaleva .... 270 276
Separation of Uranium from Impurities by Means of Ammonium Sulfite. N. P. Galkin and
G. A. Polonnikova ......... ................................. 272 277
Quantitative Spectral Analysis of the Isotopic Composition of Boron.
B.-,V. L'vov and V. I. Mosichev ...................................... 274 279
IX Session of the Learned Council of the Joint Institute for Nuclear Studies. V. Biryukov .... 278 282
Conference on Representatives of 12 Governments. V. Biryukov ...................... 282 285
Symposium on Inelastic Neutron Scattering in Solids and Fluids. M. G. Zemlyanov ......... 282 285
Symposium on Physics Research with Pile-Produced Neutrons. A. M. Demidov ..:......... 284 287
[International Colloquium on Electrostatic Generators
Source: Nucl. Engng. 5, No. 54, 524 (1960) ............................... 288]
[Second International Accelerator Conference
Source: Nucl. Engng. 5, No. 54, 523 (1960) ............................... 289]
International Colloquium on Radioactive Isotope Applications in Construction ............ 286 289
West German Atomforum Conference. Yu. Mityaev .............................. 287 291
[Problems of Uranium Geology and Geochemistry Reviewed at the Convention
of the US Society of Economic Geologists ............. ............. 292]
[First Results of Studies on the CERN Proton Synchroton ........................... 293]
[Revised Swedish Reactor Building Program
Source: Nucleonics 18, No. 12, 30 (1960)..... ........................ 294]
[American High-Temperature Gas-Cooled HTGR Reactor
Source: Nucl. Energy No. 150, 539 (1960) ............................... ? 295]
[The Nestor Research Reactor
Source: Nucl. Engng. 5, No. 54, 506 (1960) ................................ 297]
[Amalgam Methods in Nuclear Engineering ...... 299]
[Isolation of Pure Beryllium Compounds, Technique Based on the Insolubility of Basic
Beryllium Acetate
Source: Chem. and Engng. News 38, No. 39, 112 (1960) ...................... 300]
[Removal of Strong Acids from Solutions Using Sulfate Anion Exchange Resins
Source: Chem. and Engng. News 38-, No. 39, 67 (1960) ....................... 301]
[Ion Exchange Method for Holdback of Ions
Source: Chem. and Engng. News 38, No. 39-(1960) ........................ 301]
Brief Communications . . . . . ..... . . ...... 289 302
BIBLIOGRAPHY
New Literature .................................................... 290 304
The Table of Contents lists all materials that appear in Atomnaya i nergiya. Those items that
originated in the English language are not included in the translation and are shown enclosed in brackets.
Whenever possible, the English-language source containing the omitted reports will be given.
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THE SELECTION OF THE OPTIMUM PARAMETERS FOR AN
ATOMIC ELECTRIC GENERATING STATION
A. Ya. Kramerov
Translated from Atomnaya,Energiya, Vol. 10, No. 3, pp. 211-221, March, 1961
Original article submitted June, 1960
A system of equations has been derived, giving a set of optimum parameters for an atomic
electric generating station, which insure minimum cost of the electrical energy produced. It is as-
sumed that the layout, materials, and type and elements of equipment have been previously se-
lected, and that the problemis one of finding ,the optimum numerical values of the constructional
and operational parameters of the elements of the station. Quite general approximate relation-
ships are used to express the costs of the elements of the installation as a function of the parameters
being sought. Attention is paid to the mutual relationships which exist among the parameters,
through the equations which describe the processes going on in the station, as well as to the limita-
tions which are imposed by the need for reliable operation.
The system of equations derived may be used to check the optimum parameters of various
projected two-loop installations with nonboiling reactors, employing the maximum allowable
fuel element temperatures. Examples are given to show the importance of the independent prob-
lem of expressing some of the optimum parameters in terms of other parameters obtained from
individual equations of the system.
General Conditions of Minimum Cost
The minimum cost of electrical energy occurs for the condition that the partial derivatives of the. expression
for the cost of 1. KWH (ce), taken with respect to the independent parameters xk, are equal to zero, thus:
1lnx~e cCi-(1 + n) N, { n;llint=U. (1)
Since the xk's are independent parameters the problem is to calculate the relations Pm(xk) = 0 existing between
them, which describe the physical processes taking place in the atomic generating station and thus give expression
to the limiting conditions insuring reliable operation of the station.
In Eq. (1), ce= ~n e is the cose of 1 kw-hr of electrical energy produced (here No = Nb- Nint is the
useful electrical output, equal to the difference between the total output Nb and the internal losses Nint,C = ECi
is the cost of building and operating the station over its normal period of productivity T,? including fuel consump-
tion); ci = Ci/C is the fraction of the total cost C represented by the ith component Ci; n = Nint/No is the fraction
of the energy consumed in internal losses. The logarithmic derivative of a quantity Y with respect to xk will be
designated from now on by Y' = a In Y/a In xk; thus: Nb = a In Nb/a In xk and Nint = a In Nint/a In xk.
It follows from Eq. (1) that the logarithmic total differential of the cost of the station must be equal to zero
for optimum parameters, thus:
d In ce = = ~' 1%,td In x;t = ().
? It is to be understood that this period is not equal to the period of amortization of the equipment of the station.
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The deviation of a given Fk from zero is a measure of the fractional increase in cost per kw-hr over the minimum
value, which is a feature gained by the use of "logarithmic" derivatives in the present paper.
Equation (1) gives the optimum parameters, which, generally speaking, may not satisfy all the inequalities
' m (xk) -"< 0, which represent possible conditions for the construction and reliable operation of the generating station,
but which are not taken into consideration in setting up the system (1). These inequalities should be replaced by
equations; i.e., they should be used as "limiting" conditions and included among the conditions which are considered
directly in looking for the optimum. If one of these conditions actually limits the system, it may have to be revised
accordingly, and solved-anew.
The Relation of the Cost to the Parameters
In the following discussion it is assumed that the various types of elements in the station have been decided
upon; i.e., the decisions have made as to suitable constructional layout and scheme of operation under the given
conditions, the materials to be used, the number of parallel connected units,etc. Under these conditions, the cost
of an element of the generating station is determined by the weight of material used and the complexity of fabrica-
tion, which, as a rule, depend only slightly on the parameters, except in those cases where a parameter change is
accompanied by reducing the dimensions of an element down to something smaller; for example ,changing the diam-
eter of the fuel elements, which affects the cost of the fuel. In a rather well-known way, all this justifies the further
step of representing the cost Cl of an element of a fixed type of generating station in the form of a polynomial in-
volving the weight of Gi, in particular the polynomial of the first degree:
Ci kiiGi ii'" Chi + kiGti =
= a constant part (depending on the type of element) + a variable part (depending on the parameters, through the
weight of the element), where kij and n are constant coefficients: Ci = k10 represents the constant components of
the cost: nio = 0; kil = ki; nil = 1. Having assumed a linear relation between cost and the weight of equipment of
fixed type, and bearing in mind that for a fuel cycle without fuel recovery the cost of 1 kg of fuel element depends
linearly to the degree m (with m -' 1) on the enrichment X of the fuel (term in X) and on the surface of 1 kg of
fuel element to the degree r (term in the fuel element diameter dfe), we obtain, instead of Eq. (1), the expression:
Fk = - a~Q' + aintlV nt + cfue `Y +cSG cipi f cIiAil - cTI"-cA ssrd FE +
+ so + l' S= 0'
cRCRT_ +cPLPLrL
where Nb = Qn b; N'b; Nb = Q' + n b; Q is the heat output of the reactor; b is the gross efficiency: aQ = n + 1-
(cT +cSTGI) = n+ ck+ cR *cSG + I + cBL; an = n + 1 - cEL; and aint = n +. cP are coefficients equal to the frac-
tional change in cost of 1 kw-hr of electrical energy, corresponding with unit fractional change in heat output (aQ),
efficiency (an ), and coolant circulating losses (aint) respectively; l a/L is the fraction of the total reactor length L,
proportional to the length of the active zone 1; cEL is the variable part of the cost of the electric generating installa-
tion; cSTGI = cEL + cSTGI + cSTGI is the variable part of the cost of the steam turbine generator installation (STGI):
cP = cP + cP is the variable part of the cost of pumps; cSG = cSG + PG + SII is the variable part of the cost of the
generator; cR = cR + cR is the variable part of the cost of the reactor, cx = c" + cP is the variable part of the
cost of piping in the first heat-exchange loop; c i = cRmR + cSGmSG + cP mp + cPLmPL is the sum of the effective
costs dependent upon the coolant pressure in the first heat-exchange loop taking account of the degree of depend-
ante mi; cII = cmSG + E cSTGImi is the same thing for the elements which carry the pressure of the working
part of the second heat-exchange loop; cE is the cost of the nuclear fuel (heating material) consumed during the
period of economical operation; cFE is the cost of the fuel elements consumed (along with the replaceable parts of
the fuel channels); cASS is the cost of making up the fuel element assemblies, consumed during the period of eco-
nomical operation.
The meaning of the superscripts on the c's is as follows: x - variable part of the cost; v - variable part of the
cost, which is proportional to the dimensions (volume) of the element; p - the same, but including the proportionality
to the pressure by the factor m. The subscripts show what element, system, or process the c's belong to, thus: I
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first heat exchange loop; II - second heat-exchange loop; R - reactor, P - pump. The fractional costs, ci, represent
the fraction of the total cost of construction and operation of the station given by:
The components entering into the optimizing conditions are the logarithmic derivatives Y', taken with respect
to the desired independent parameters xk, of the quantities Y, which serve to express the cost and the output. Some
of these are "elemental" geometric quantities, such as the cross section of the reactor So, the diameter of piping SPL'
the equivalent diameter of the fuel emenets dFE, and the length of the active zone 1 , some may be operating quant-
ities, such as the pressure pi and p11 in the first and second heat-exchange loops; some may be physical, such as the
enrichment X, and the degree of burnout G; but at any rate they are good variables to use as the independent param-
eters that we are looking for;;?the process being that the derivatives in question go to zero, except for the derivative
of a given parameter with respect to itself, which is equal to unity, thus:
Y'- xi - 8 1 n xl -0 for k r l andY' = 1 for k=1.
0In xk
The remaining Y values entering into Eq. (3) - the heat output Q, the steam generator surface F, the station effici-
ency, ti , and the internal circulating losses Nint - are all functions of the directly determined geometric, operational,
and physical paramaters " and in this sense are "secondary" parameters of the atomic generating station. Therefore,
in what follows, we shall simply let these values be determined through the primary parameters as these are governed
by the limitations placed upon them by a two loop generating station using nonboiling reactors. At the same time
we are looking for their logarithmic derivatives Y' = a In Y/0 In xk (entering into the condition Fk = 0), which are
the coefficients standing before (d In xk) in the, expression d in Y = EY'd In xk. Substituting these derivatives into
k
Eq. (3) yields the desired system of equations, defining the relations between the optimum parameters.
Relations between the Primary and Secondary Parameters of the Atomic Generating
Station
The relations between the parameters and the limitations placed upon them depend on the laws governing the
physical processes taking place in the generating station, as well as on the constructional possibilities and the de-
mands of reliable operation. The following results have been obtained from these relationships after a number of
transformations and familiar simplifications.
Reactor heat output.
Q=Gc( max-Ts)1-1
)din'EFE {-x(1-B)dlndFE +x a dine+xBdInS..
c is the heat capacity of the coolant; Tmax is the maximum temperature of the fuel elements; Ts is the boiling
point of the working fluid in the steam generator; f = K - b ip - b ii x (XF -1)"1 is a coefficient equal to the ratio
of the maximum temperature difference in the first loop (Tmax - Ts) to the coolant temperature rise in the reactor,
AT = T1 - T2 (where T2 is the temperature of the coolant on entering the reactor, and T1 is the temperature on
leaving the reactor); K = KOTK e = (Tmax - T2)/AT is a coefficient in which KAT = ATmax /AT expresses the non-
uniformity in coolant temperature rise along a reactor fuel channel, a quantity which is practically independent of
? It should be noted, that in a ,number of cases, the enrichment X is more conveniently determined as a function of
other parameters of the reactor, which have to do with insuring criticality.
dInQ=(1-xB)dInG+TTmaxTdln max-T Tx d'1nTs-&Fd1nXF-
max s max s
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the choice of parameters which we are discussing; K 9 = (Tmax TO /ATmax is the coefficient of overheating of
the fuel elements, which, for a fixed distribution of fuel elements along the fuel channel depends only on the simple "
ratio y = /Tmax/9 (as can be seen, for example) from dimensional considerations; 9 is the mean temperature dif-
ferential between the fuel elements and the coolant; K K/f K' = K If x o In K/ a In y; f XF = a In f/a in XF
and B = (1 - St' ) h/a -1- are coefficients determined by the thermal engineering" of the first loop of the reactor;
.St' = a In St/8 In Pe; St a /wyc is Stanton's criterion; Pe = RePr = wdyc/A is Pekle's criterion; a is the coeffici-
ent of heat release from the surface of a fuel element to the coolant; h is the coefficient of heat release to the cool-
ant from a point on the fuel element where the temperature Tmax is reached: 6 FE = SFE/So is the fraction of the
cross section of the active zone So occupied by the cross section of fuel elements SFE; e = S/S0 is the fraction of the
cross section of the active zone So occuped by the cross section of coolant channels S; dip and 611 are the fractions
of the heat going into heating (6 ip = Dip /ii) and evaporating (6 11 = iii /ii) the feed water to the steam generator;
XF is the degree of cooling off of the coolant in the evaporational part of the steam generator (see below).
The value d In Tmax = 0 holds. except for the case where the maximum surface temperature of the fuel ele-
ments is limited by the boiling point of the coolant; thus: Tmax = Ts(p1)? In the latter case (for water) we can use
the empirical expression:
Ts-273=to-100Vp,
dIn Tmax =dIn7's (Pr) L-- 4 Tg(1)-273
8 (PI) d In pI.
Steam generator surface F. The exact expression for F and its partial derivatives with respect to the desired
parameters is fairly complicated, since there are different components in the steam generator with different heat
capacities and different temperature differentials 6 j, including the heating differential 9 P. the evaporation
differential 01, and the superheat differential 9 SH? Simpler expressions are obtained by leaving out the heating and
superheat components, or by equating the evaporation and superheat differentials. Then the mean temperature
differentials will be equal for all these components; thus: 6 j = A p = ii = 9 SH = 6 li (iT/ln XF) and the expression for
the surface of the steam generator takes the form:
p, -` 1, _GcAT 8ii Ge 1nX
$' I a3 aSi . F
i i t
XF _ T2+(1-6iSH)AT-T9 - temperature differential entering evaporator
7'2+Sip1T-7'g temperature differential leaving evaporator
i.e., "the degree of cooling off" of the coolant in the evaporating part of the steam generator; a = (1r b ij /a j )-1
is the mean heat transfer coefficient in the steam generator; 6 ii = Ali /E iij is the fraction of the heat transferred
in the jth component of the steam generator.
From Eq. (6), taking 6 11 to be constant, it follows that
din F=dInG+dIn (InXF)-dIn a.
For constant diameter and spacing of the tubes in the steam generator we can write
dIn a= 0In1?e dIn Re =aRe(dIn G dInSSG),,
where the criterion is given by Re = wdg /v = G/SSG dg/y v ; w = G/SSGY is the coolant velocity; dg is the hydrau-
lic diameter; SSG is the coolant channel cross section in the steam generator;' y and v are respectively the specific
gravity and viscosity of the coolant. In toto, we get the, equation (approximately correct even for 9 p 91 8 SH):
dInF=dInG(1-ale)d-aRedinSSG +dIn (IIXF).
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The efficiency , . The thermal efficiency of an ideal regenerative cycle is
where Tx and AS are respectively the mean temperature and the reduction in entropy for withdrawal of heat from
the cycle; Al is the increment in heat content in adding heat to the cycle. After rearrangement, and bearing in mind
the approximate equality of the mean heat capacities of the working fluid
T2 T(+2
5 cpoIn T 1 cpdT
Ti Ti
T2 T2
J dlnT r J dT
TI T1
we get
tlt=1-TeC.
where cP and cp are respectively the. mean heat capacity of water and vapor; OtSH is the superheat of the vapor.
In the absence of insufficient heating of the water or superheat of the vapor (Atp = ztSH = Sip S 1SH = 0),
the correction factor c in Eq. (8) is equal to unity.
Usually (c - 1) Ta E m
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3 titles of, i,mm,ediate"in-terest!
Order from.
LECTURES, ON NUCLEAR THEORY
by L. Landau and Ya. Smorodinsky
Translated from Russian ,.
A concise presentation by these world-famous Soviet physicists of
some of the basic concepts of nuclear. theory. Originally published
at $15.00 per copy.
a real jewel of an-elementary introduction into the main con-
cepts.of nuclear theory ..."-NUCLEAR PHYSICS
fl. . a decidedly ,worth-while addition to any, expkerimental nuclear
physicist's library."-E. M. Henley, PHYSICS TODAY
cloth 108 pages $5.25
PLENUM PRESS 227 W. 17th Street; New York 11, N.Y.
- of major interest to all researchers in low-temperature physics.
A SUPPLEMENT ?TO "HELIUM"
By.E.. M. Lifshits and`E. L. Andronikashvili
Translated from Russian
-This notable volume consists-of two supplementaty chapters, by
these outstanding Soviet physicists, which were added to the Rus-
sian tfanslation of W. H. Keesom's classic book "Helium."
The first chapter, by Lifshits,, presents a concise resume of the
Landau theory of superfluidity. The- second chapter reports in con-
siderable.detail the -experimental work conducted by Peter Kapitza
and E. L. Andronikashvili.,
cloth 167 pages illustrated . $7-50';
- " 4
Order from: CONSULTANTS .BUREAU ' 227 W.' I7th'St. ? New York 11, N. N.Y.
The Soviet authors put forth a systematic presentation-of a new
method 'in the theory of superconductivity, developed as a result of..
A NEW. METHOD IN THE THEORY OF-, 'I I
SUPERCONDUCTIVITY -
By. N. N. Bogoliubov, V. V. Tolmachev and, D. V. Shirkov
Translated from Russian
f
the research of N. N. Bogoliubov and V. V. Tolmachev-based on
a physical and mathematical analogy with superfluidity. This new
method is an"immediate generalization of-the method developed by
Bogoliubov in formulating'a microscopic- theory of superfluidity.
The authors give calculations for the energy of the superconducting ground state using
Frohlich's Hamiltonian, as well--as- of-the'one-fermion and collective elementary excited
states. A detailed analysis of the. role of the Coulomb interaction between the electrons, in
the theory of superconductivity is .included. The authors also demonstrate how a system
of fermions is treated with a "fourth-order interaction Hamiltonian and establish the cri-
terion for its "superconductivity.
cloth , 1121-pages, illustrated $5.75
Order from: CONSULTANTS BUREAU.- 227 W. 17th St. ?' New York' 11. N. Y.
Descriptive folders upon request.
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RESEARCH by Soviet
EXPERTS
.SPECTRA AND ANALYSIS.
. by A. A. Kharkevich
.The "first handbook directed toward acousticians, and others work-
ing in those fields which require the analysis of oscillations-
ultrasonics, electronics, shock and vibration engineering. This
volume is devoted to the analysis of spectral concepts as they are
applied to oscillations in acoustics and electronic engineering, and
to a discussion of the methods of spectral analysis. Contents in-,
elude KOTEL'NIKOV'S theorem for bounded spectra, the spec-
tra and analysis of random processes, and (in connection with the
latter) the statistical compression of spectra.
cloth 236 pages $8.75
ULTRASONICS AND ITS`
INDUSTRIAL APPLICAT-IONS'
by 0. I. Babjkov
This work is concerned with ultrasonic control methods which- are
applied in industry, and also with the action of high-intensity
ultrasonic oscillations on various technological processes. Con-
siderable attention is devoted to ultrasonic pulse methods of flaw
detection and physicochemical research. It" is an invaluable-aid
to scientific researchers, engineers, and technicians working in
fields which make use of ultrasonic methods industrially, as well
as being a convenient, reference for a broad category of readers
who might wish to become. acquainted with the current ,state of
ultrasonic instrumentation.
cloth 265 pages $9.75
Tables of- contents upon request
227 West 17th Street * New York 11, N.Y. e U.S3M
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