SCIENTIFIC ABSTRACT SOKOLOV, A. - SOKOLOV, A.A.

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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

SOKOLOV, A.
"On the Dipolness of Mesons and the Difficulties of the Proca lbeory," Zhur
Eksper. i. Teoret. Fiz., 12, iio. io, 1942.
State University, Sverdlovsk.

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On ft Smy d Wimlidmit. L IwAmmmo. D..
Am Soamow, A. J. Fkm. VSSJL 9. 1. pp. W35,

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SOKOLOV, A.
194-4.
"On the Theory of Bi-Particles. II," Zhur. Eksper. i Teoret. Fiz., 14, No. 10-11,
FhYSiC5 inst., Moscow State Univ.; Sverdlovsk State Pedagogical Inst.

MV
I
01,
cWfton waves. Acad.
On the potarization of
Phys, 9, 363--372 (1945).7 w'122],
The polarization of election wavest's bivestigated for the
cases of refle ion froll
-et 1 .1 poteattal birrier .
- and of scatwring
by a center of force' For the Livo-dimensiotial problem of
the reflection and refraction of plane electron waves by a
stet)-function twteotfid whose magoilude is small comi)ared
e -it both
to the kinetic encrgy (Sf tht! lt.~ctron, it is Shown tit,
the reflected and the refracted wams are unpo)arized if the t
incident wave is unpolarizvd. For the problem of scatteriog
by a center of force, a gelleral foraltilit is first derived by
using Dirac's tinic-dependitut pvrLtirhalion theory and itis
then applicil to the, cn-,L wlivre the force center possesses
electric charge and magnetic moment. Siuce the existence
analysis of the
of polarization can only I_- detected by
scattered waves by another sa:atteritig prmcss, the distribu-
tions for double scattering 1)), two centers of force are
calculated. It, is shown that in the-first approximation
ation terms occur only.if the scattering centers possess
polari&
both electric and magnetic moment, neidwr the charge or
the moment by itself being sufficicat. When the calculation
is carried out to the second approximation, )urL Coulomb
interaction gives rise to 1w)[arizatiott effectsand (It(! (ormula
obtained here coincides with that obtained by Mott pre-
viously in a different way. Kiesaka (Princeton, N. J.).
_01
Source: Mathematical Reviews. Vol No
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Sverdlovsk State Un:Lv. -

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Sokolow, A. A. On the classical theary'af eleinent=7_ i

lectron). Vestnik Aloskov. Univ-. 1947'.
IZUTO_Mnre~
paru
no. 2, 33-43_(FT7T__TRussian. E-aglish summary)
The enuation of moti n of a classical point electron,
including the radiation-reaction tetin, is derived by a pro-
cedure essentially the same as that used by P. A, M. Dirac
[Proc. Roy, Soc, London. Ser. A. 167. 148-169 (1938)] ind
G. Wenuel CZ. Physik 86, 479-49-1 (1933)]. The,author
does not refer to the recent and more profound analysis of
this procedure by J. A. Wheeler -arid R. P. Feynman [Rev.
Modern Physics 17, 157-181 (1945j-r]. lie includes a brief
discussion of the problern of fixing boundary conditions so.
as to exclude the nonphysical self-accelerating solution's of : I . I.
the equation of motion, and. also derives the formulae for i
the emission and scattering of light by an electron.
F. J. Dysbyl (London).
%t

Source; Mathematical Reviews, Vol 'No.

SOKOLOV, A. A.
105. A. A. Snkfilov On the rolution of the tionlitinir
mech-nical equation by the perturbation method ~in ltn-~~;mi
with T_n7i-h gilpimary), Vr-itnik Nfriskov. Univ. 10:7. no.
77-82 (19 17).
Thn withor treittit lliv equation dosetibing the (athaNitic)
motion of it nmi in n hibe with oi)plfixrd end and with it firs4y
moving j)Wnn of masq A/. The. differential equatint) reildi:
I'll,? irillitil condiflons are: 0, mit.
n1flok (fit, 1 1) r, r I a. Tilt, boundary condiflowt nra:
t - o fftr.r 0. t,_ - (jt!a)t~, forr. - a. llero t In tilt! firujilihidtf
r 1111d I 1'11~rnli ginn vnrI;t1)Ivq' e. (lift swollittiv. Kjw't~ll fol 0111 ("lift.
.3timf.) initial 4(ate, 'Y (If(! ratio of sim,fle hen1a, a tilt! 11,11110 diq-
tilurv froin fhv. piqfon to file fixed end, g ~ ?n/(-Yjlt), m In"Ing 1,110;
Phiins.
rlms!l or tilt' glAs jef. A. 8. F. Love and F. B. Pi(
Tratiq. Roy. SIC. 1,011do'=7r. ins-22r, (1922)1. Argunt-'
Ing an expansifin in powet-ti of g and neglecting u1 and fer"is of:
higher ordr-ir, the, aufflir libt4iins an approximato solution (if tho'
form + u, Ifere t2 x - (ju/(3)(x rl/al)
~.,6 defermined by the relation
t,)j1/(2v)j. ror
small values of 1, ~t I + kill".; fo~ large valuca of 1, (2t,L)VII.
Tha formulm for the additional torm u are too coin pi icated to hr.
reproduced here. This tcrm reprenents a standing wavo which
disappeam An I w. T,. BQm, USA

1~ A
Mewitabte combinations ot elamentat particles, 1). -
1). A. A. Sokolov. VejImsk 3faikor. I'mir.
1947. No. 6, 3-7.--Cro~, sectimn am calcd. for the cuuj-
bination of a rue-ion with an electron of opposite sign to
forni a metastable "planetary" system at various velocities
-1
IJ
r of the incklent particle. When r < at (where a is the
k
;uIe-Itructurc const. and C is the velocity of light), the
cs~, -~-ction is comparatively high. when v - c. forma-
tion of this system And annihilation are equally probable.
For r > or, annihilation is more probable. The life of'
mich a Ytcul is caled. to be -5 X 11) -Is see. C. F.

Ivantaiko, D. D and Sokolov, A. A. Quantum th=of
1947,no.8,103-1
gravlation. vestn 13
(1947). (Rus5ian)
Th -e paper begins with a simplified derivation of the
equations of M. Fierz and W. Pauli [Proc. Roy. Soc.
London:Ser. A. 173, 211-232 (1939); these Rev. 1, 190]
describing a quantized field of tensor character. Such a field
can be identified with the Einstein gravitational field, in
a weak-field approximation neglecting quadratic terms in
the field equations. The quanta of the field, "gravitons,"
are particles of spin two. The intensity of gravitational -
radiation front a moving source of the field is calculated
by perturbation theory, and is found toagree with the
classically calculated intensity in the low-frcqtiency limit.
Finally, there is consid -ered the problem of a quantized
scalar field acting as the source of the gravitational field;
in this case there exists a process of annihilation of a scalar
particle and anti-particle, with the emission of two gravi-
tons; also there exists an inverse process of creation. The
cross-section for the annihilation process is found to be of
the order of the square of the gravitational radius of a
scalar particle. F. J. Dysart (London).
So-arcs t MathemUcal P-6viewsi vol tO No. .7

U, K 11; L.- U- V
UL-)O"R/h'u&lear Physics - Particles, Elementary
Nuclear Physics - Stability
Dee 47
"Metastable Uompounds of Elementary Particles," D. Ivanerko Phys Inst ?'.;oscow State- U
imerd It. V. Lorronosov; A. Sokolov, Agr Acad imeni K. A. Timi'ryazev, -X pp
"Dok Akad Nauk SSSR, Nova Ser" Vol LVIII, No 7
Discusses systems whose stability is result of electric forces. Explains reliability
of formaticn of atom type atoms from two elementary particles. Sub?,dtted by Academician
S. I. Vavilov, 24 Jul 1947.
PA 60T81

SOKOLOV, A. A.
Sokolovi- A. A. - "Toward a theory of the luminous electron," Vestnik. Mosk.
un-t.a-, 1948, No. 11, P. 0/5-101 -- Bibliog: p. 101
So: U- 3566, 15 March 53, (Letopis Murnal ! nykh Statey, No. 132 1949)

,3,'~KOLOV, A.
USSR/Nuclear Physics - Electrons, Emission of Sep/Oct 48
Nuclear Physics - Electrons, Acceleration of
"Theory of the Luminescent Electron," D. Ivanenko, A. Sokolov, 1/8 p
IIIz Ak Nauk SSSR, Ser Fiz" Vol XII, No 5
Describes results of authors' work on calculating the emission spectra of electrons
in activators (A. Sokolov., "Vest Moskov U" 4, 77, 1947; D. Ivanenko and A. Sokolov,
IIDok Ak Nauk SSSR" 58, 1948). ZT-his is a complete translation.-
PA 19A9TIO7

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1691 The Theory of the Point Ilectrom 10 A. A. Sokolov.
-
X~tjgh-lm; ligiff 18
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pe
,
1948. (In apastan)
An Investigation is modo of a "rise of questions masoclated
with the classical theory of notion of point electrons.

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Ime. 08 of &OW? of Or "hMisim" dMIN 9wra
distribution in ordinah of the hsrmOqicI,. The Imllff
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1,4-,mNsLo. D. AND SotEoLov. A. "L .4kkL M".
r0rMuld is inconveneent as the harmonic ordinal
:
AS-Nk " (NO. 9) 1551-4 MM) In RauiAe.-A fufi numbers &Rmr as arippment and as ondftiig of 41
:
r thcoq ofthe; c.m. radiation from citLtrons amicroted Pl"wl functiOm as vmll. The methods of approxi. 00
i it) - I0'cV In bmitrona is lp-ma, As aw lawasitics nution of Brillouin. Wcntml and Krantert, apo*d 10 =00
of higher MUllipOICS Of the Order R AIC Obtained by 3 s""id Order d1ir equation ykid & good appruji.
multiplying the dipok inkerAity by n. consideration mation far faille values of the Afturnent. A rmthod
of velocities may simply be based on given pmv!oWy by onc of the Authors etuble, th

j
dopok radiation. The ultra-rclatMstic cax. ho%%- e
approximation to he extended over the vshok rW
9
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ftb
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b of Yalu" of the argument. i.e. to exclude discon-
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of the vector potential by aid of "nung's vector nu
t
c3. Two extretm ases Are then dix'uwd and
on c2prcsAion for the rAte at' cncr&v dereese at
I 51~ Ind d* CnCW distribution of the n-th harmonic) e%t-ly, high (mquencics is &Iis,,d. IL F. K.
and mornmation yields tM distribution of the radiation
in IpKv which is practically concentrated in a plane.

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Moscow State Univ. im. M. V. Lomonosov, Agr. Acad. im.
K. A. Timiryazev.
I L A *ITALLIPfKAL LITERATLIBE CLASWICATIC~
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SuKOL6,71. ~i.
USSIR/Nuclear Physics - Cosmic Radiation
Nuclear F-Ilysics - Particles
Jul 46
icor
y of Para- and Ortho- State of Elementary Particles," D. Ivanenko, A. Sokolov,
Phys Inst, Noscow State U Imeni I'A. V. Lomonosov, 3 PP
"Dok ilk Nauk SSSH" Vol I~CI, No 1
According to a recent hypothesis, when a f.-ee electron and a positron collide, a
metastable system (a positroni) consisting of two particles revolving about a comrion center
of ~zravity occurs concurrently with annihilation. in a positroni aton, one must
distin;7uish between systems with parallel (orthopositroni) and antiparallel (para-po5itroni)
spins. Inasmuch as: the life span of a positroni, must dpend on the total spin, the
question of investipation the nara- Ind ortho-systems of a free electron and a
positron naturally arises, especially as the difficult problem of annihilation of the
para- and ortho-positronis may be connected with the amihilation of free particles,
since the energy of co.qb-nation of a positroni Ls jj!any times less than the individual
ener.-y of a positron or electron. Authors discuss questions with aid of Dirac's matrices
and Casimir's formulas. Sulxditted 15 Apr 1948
PA ~IL9 U01

SOKOLOV, A. A.; IVAIIENKO, D.
Claw3lcal '11wory of Flalds (14oucow -Leningrad, State Technical Press, 1949.
Feviewed by 14. F. Shiroko7, Sov. Kniga, No. 8,
Report U-3081, 16 Jan 53

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AC)PI31

S C"U, L C
USSIR/Nuclear Physics Menotrons. Jan 49
Nuclear Physics Cosmic Rays
"The Mass of Neutral Mesons," A. Sokolov,
B. Kerimov, Sci Res Inst Phys, Moscav State
U imeni M. V. Lomonosov, 4 pp
"Dok Ak Nauk SSSR" Vol LXIV, No 2
Entablishes that the mass of neutral mesons,
being brought into equilibrium vith a
system of nucleons, cannot exceed the value
130 m (m = the mass of one electron). Sub-
mitted 6 Nov 48.
25/49T80

UM/Ruclear Physics Lamimecent Aug 49
Ilectron
Electrons,-Acceleration
0
CD
0
4~0
"The Quantum Theory of the Luminescent Electron,'
A. Sokolov, Sci Pas lust of Phys, Moscow State U
imeni M. V. LomonosoT, 4 pp
"Dok Ak Nauk WSM" Vol LKY I, No 6
An electron rotating around a periphery, e.g.,
in cyclotron accelerating devices, becomes
a source of electromagnetic radiation. The
radiation intensity of higher harmonics Is in-
significant for nourelativistic electron speeds.
Im
1/50760
USSR/Ruclear Physics - Luminescent Aug 49
Electron (Contd 1)
For electron speeds approximating the speed of
light, the naxinum radiation intensity lies in
the region of the harmonics: no approximately
equals (r/mc2)3, where I is the energy of the
rotating electron, and a is its mass. For an
electron of sufficiently high energy, the fre-
quency %v (noonega) may fall in the visible
part of the spectrum, this being called the
phenomenom of the luminescent electron. At-
tempts to find the influence of quantum cor-
rections upon the curve of spectral radiation
and the limits within which the classical theory
low 1/50760
USSR/Nuclear Physics - Luminescent Aug 49
Electron (Contd 2)
may be applied to the luminescent electron.
Submitted by Aced S. 1. Vavilom 25 Jx;n 496
1/50760

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i An ape"malo evaeftl torinals to dorl"d for W --crit.
"
leal
numintra N of swelfuna completing successive nuclear
sholls as a (section of iM Isarlosaw denolty p. The statistical
of Fermi. wbkb Me W ead, bews, employed f" the
approalmais doduction ol critical twinto a of olearono in an
atom. was folkwoIl. Tlw statistical Modell IGMS directly to
the t"M%I*N - (11 8"Op. Asentijk4corlOndisIrl-
button of p, t1w N's attt uWWW owt sively for I - o, 1, 2,
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p Is sa4umM to vary cinkismovely in space, III# nundwrm 4i
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AnAPPfulklmAlf. P10111111017 U111, 0111. do Millis should
Do rallarded as irl" only a teflab auteral anstwor to the
00 A problem. Corrections. Butts as tMt low I%& Costomb Inter.
action between protons. or that fw VA ~ of tlW surface
layer, could be Istroillocd. Vale", (Phys. Rev. 7 . 77(1950)),

I in an analysis al the *mpjrk&UV kamm series 01,, _at,
numbers. atitatnod the foraggs N
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to that elven above.
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S~OKOLOV, A. A.; 111ANETIRIO, D. -:J.
Classical Field Theory 'w'Klasicheskaya Tecriya Folya). This is the second edition,
Dublished in 1a'51 and has 47r~ T~ es.
~ I a.,;

,-TOV, 1. ~.
H -KOV, DAADNEA, 3. 1., -Tj,r ,
K~- A !I MA-1 A v 0 U
.jOV, 3.
,. (I~ji,or), AKIIL:,-GV, 3. N.
(Tech. ro:ditor), and FEYNKRG, Ye. A.
D. I. Blokhintsev, "Fundamentals of Quantum Mechanical', Osnovy Kvantovoy
Mekhaniki, State Press for Technical-Theoretical Literature.
Table of Contents Id-17671, 5 Apr 1951

SOKOLOV ,
"Optical. Propertie5 -)' "'etal 'lloys in the Infra-Red Regior of the Spectrum." SOKOLOV
~T I 1.1()y I
and othei-3. "ZIMFINAL 'EKSPEIRDTINT ~ TEOPYTICH-E-SKOY FIZIKI" 4/19c,2-

Mathematical Reviews'
VOL 14 No- 10
NOV- 1953
Mathematical Fbysics~
*Sokolov, A., I Ivanenko, D. Kvantovaya teorlya polyiL
(Izbrannyo voprosy.) [The quantum theory of fields.
(Selected questions.)] Gosudarstv. lzdat. Tehn.-Teor.
Lit. Moscow-Uningrad, 1952. 780 pp. 1 4.30 rubles.
The book consists of two separate parts. Part 1, "Quan-
turn electrodynamics" b)!).A. Sokolov (pp. 9-480), is based
on a lecture course for students specializing in theoretical
physics. Particular consideration is given to papers pub-
lished in Russia. Knowledge of the authors' "Classical
theory of fields" [2nd ed., Gostehizdat, Moscow-Lenin-
grad, 1951; see these Rev. 13, 95 for a review of the Ist ed.]
is presupposed. The quantum theory of the electron and of
the electromagnetic field is presented in the way customary
a
:1 before the use of the interaction representation. Tjtc qu, n~
turn theory of radiation is developed in considerable detail
anq applied to a number ofSroblems. (This bectiop of Me
book is about equivalent W'Ileitler's "Nantuni theory of
radiation" [2nd ed., Oxford, 1944].) The theory of pmi-
tronium and of cosmic radiation irocesses is outlined. A
chapter on the theory of the vacuum covers tol)ics hardly
accessible elsewhere in textbooks, like self-energies, rekLll;kr-
ization methods, radiative corrections, L"Imb-shift, infrared
catastrophe, etc. There is also an intertstinx liaragralib oft
the domain of applicability of quantum theory whure the
Soviet point of vic%v of the interprelittion of citiantIIIII
mechanics is presented., We read,for hist;pirt!, int, ). lh,l:

USSR/Physics - Gravitational Field Sep 52
"Remarks on the.Quantum Theory of A Gravitational
Field.,"IA. A. Sokolov, Moscow State Univ, Chair
of Theoretical Physics
Vest Mos Univ, Ser Fizikomat, i Yest Nauk, No 6,
pp 9-20
Attempts quantization of gravitational field by
considering a weak gravitational field, the eq of
which allows one to neglect terms of higher order.
Demonstrates that in linear approximation eqs of
gravity may be classified into the general scheme
275T107
of elementary particles, consisting of neutral par-
ticles with zero rest-mass and spin of two. Dis-
cusses existence of two-dimensional gravitational
waves. Rec 30 Apr 52.

SOKOLOV. A.A., professor.
Train highly qualified cadres of physicists. Vest.Moak.un.8
no.12:9-15 D 153. (KLRA 7:2)
1. Dekan Fizichaskogo fakul'teta. (Physics--Study and teaching)

u S
537.533.9
8349. On of a luminescent elte.
the quatuturn th
tron. H. A. A~-Sdwxoy,
-211. iksper. MO. Jqz., 24, No. 3,
(1953) In Mussiatt.
in continuatiort of Pt 1'[Abstr. 528 (1954A the
atithors find the wtal intensity of radiation, assuming -
Th-- fin-M cquation is
E )' +
16 mcR im"
of classical orbil, and E - CICCLFOQ
15c.: aho Abstr. 8224 (1953)1. F. LACUMAN

539.153 537.12i.131
For-matir-, caf miAswe cq%j%wjd2 from,
A- A-
Soc
-
7.-
i~, Ci iiT
I-svrovicEl
4*spe-
A~up
rZ
;F

.
.,
.
.
.
1
.,
:'t-I., A'Usm 10~7, 4q7I (1949); 15W, 3320 (1950);
257, 2917 (1952). Disscmw the inter-
b~ml:crl ql-tlilfizcd Stites, and ft wave-
funcuons with fourth-order malrievi am converted
inEo th~)w ~~idvi ~,,-ond-or&r rnatxkxs. Approxim-alt;
are olafaiMd for tho interaction between
2 chwur!~~d partick-s and, finWy, the way.-Functions
'.Vul CrLcrL;3r of poiftranium are derivcd, thus enabling
-r-ib Ii!
th,, rk Y of fonnation of rneWtabla posi-
irorkm stati~s to Lie asscssed. Uv positronium
in magnetic fields are dismssed.
V. LXCM%IA
4
.

13, r
537,533.9
k6_15*3. ON THE QUANTUM THEORY OF A
ELECTRON. M-IV. A.A.Sokolov and I.M.Temov.
Zh. &Bper. tear.
Vol. 28, No. 4, 431-6 (1955). In Russian.
For Pt Hi see Abstr. 8349 (1954). An expression is
developed for the quantum corrections to the trajectory 0?.?
relativistic electLMln a magnetic field with axial symmetry.
F.Lachman

36n.U_L6V. ~. A.
USSR/Nuclear Physics - Deuterium Lamb-Shifit
Sep 53
"The Lamb-Shift for h.,.-dro~en and Deuterium" /translation into Russian with coPL-ents b,,r
YI.I. Shirokov-7
us
p Az Nauk. Vol 51, 0 1, PP 115-129
Translation of E. Salpeter's article in Ph.,rs Rev 89, ~2 (1053). Translator appends
6 supplementary liussian-language references on the Lamb-shift and other radiative
corrections: 1. V. F. Vayskopf, Usp Piz Nauk, 411, 165 (1950). 2. Ya. A. Smoro-
dinskiy, Usp Az Nauk, ~9, 32.5 (1949). ). Scientific abstract symposium I-Problemy
Sovremennoy 1~izikil, No 6. 1948; No 1, 1950; No 11, 1951. 4. Sdvig Urovney Atomnykh
Elektronov (Shift of Levels of Atomic Electrons), a symposium, x'oreign Literature Press.
J,joscoif, 1950. 5. Sokolov and D. D. Ivaneako, Kvantovaya Teoriya. Polys. (,uantum
Theory of the zleld), Gosie~_h~zdat (State Tech Press), Poscow, 1952# 6. W. Iaiib-,
"Fine S-t__-_uTEu~reof the -en Atom" Itranslated from English into RussiaU/, Usp Piz
hydro.
Nauk "5, 553 (1951).
264T94

SOKOLOV, A.A.; KLEPIKOV, N.P.; MNOV, I.M.
On the itiestion of radiation by fast electrons in a maEnetic field. Dokl.
Akad. Nauk S.S.S.R. 89, No.4, 665-8 '53. (KIRA 6:3)
(PA 56 no.672!8224 153)
In further developing worIks on ouantum theory of luminescing
electron (A.A.Sokolov ', DJUI SSSR, 67, 19494X; A.A.Sok~lov et al., "Classical Field Theor
(Klassicheskaya teoriy~l pola), 1951; N.P.Klepikov, Dissertation; A.A.Sokolov et al.,
XhETF,, 23, 1952) authors succeeded in computing quantum corrections to ftll intensity
of emission. Presented by Acad. V.V.Shuleykin 16 Feb 5g. 256T107
S3

3 "Al

SOX~)__OV, A. .1.
USSR/Nuclear Physics - Electrodynamics 21 Sep 53
"Problem of Motion of Fast Electrons in a Magnetic
Field,q'A'.A. Sokolov and-a.M. Ternovy Moscow
State U
DAN SSSR, Vol 92, No 3, pp 537-540
Continue the study of the motion of fast electrons
discussed previously (DAN 89, (1953)). Add quan-
tum corrections to the trajectory of motion. Pre-
sented by Acad V.V. Shuleykin 22 Jul 53.
268T85

,e) I.,
1107. On a statisticul theory of the atomic ntirleus.
11. A. A. Sovoi~(IV AND D. K. KEamov. -'h- eksper.
n,4;F;NWWWtW430-tM954) In Russitm.
See Abstr, 8511 J1954). A statistic-al Ist-order per-
turb-ition treatment tafthe =rl;y ofinfinitely extended
nuclear matter, using a mcson-t)w two-body potential
containing central and tensor forces appropriate to
2 meson fields (Ntctor and ps. scalar) of different
nusses. and coupling strengths chown to eliminate
the r-' singularity in the tensor force. Theexprmion
for the total energy per unit volume is integrated out
explicitly and the condition for a minimum with
respect to change of density is Ayitten down. If the
masses of the mesons are taken as 265m, the coupling
constants deduced from this condition are not much
less than 1. and a perturbation treatment is doubtrul.
If one bf the me-sons (vector) is 130m, small coupling
strengtiis are sufficient. W. J. SWIATIC .X1 laid

SO-OL079 A. -A.
USSR/Physics
Card 1/1 Pub. 22 18/48
Authors Sokolov, A. A. and Chernov, I. M.
Title The quantum theory on motion of a relativistic electron in an axially-
symmetrical magnetic field
Periodical Dok. AN SSSR 97/5, 823 - 826, August 11, 1954
Abstract Quantum theory of a moving electron with velocities affecting its mass
in a variable magnetic field is described. Seven references (1941-1954).
Institution floscow State University of im. M. V. Lomonosov
Presented by Academician V. V. Shuleykin, May 18, 1954

U S S -5200
QUANTUM THEORYOF THE RADIATINGSLECTRON. FV.
A. A. Sokolov and 1. M. Ternoy (Moscow State Univ.). Zhur.
-E7-',7TZ-6rot Phys.28.431-6(iaris) Apr. (rhRus5i;;F 112,
An expression to derived for the q=tuM correction to the
trajectory of a relativistic electron in aa axial-symmetric
magnetic field. (trwauth)

j
USSR1 Physics - Quantum mechanics
C"'d j/.j Pub. 22 - 16/49
kathars I Sokolov, A. A.; Matveev, A. N.; and Ternov, I. M.
r I F.MW OW -~ZIWTF"R
Title I On polarization and Bpin effects in the theory of a glowing electron
Periodical i Dok. AN SM 102/1p 65-68p May 1p 1955
Abstraot A mathematical- analysis in outlined for determining the intensity of glow
of a relativistic..electron.during its transition from one quantum state (n)
into another (hI n-v) in a constan homogeneous magnetic field. Particles
with 1/2 spin andwithout spin are considered. Polarizing characteristics'
of radiated light are analyzed with the help of Dirakilis equati6n.
Eleven referencest 3 USA, and 8 USSR (1941-1954).
Institution: M. V. Loraonosov's State University., Moscow
Presented by: Academician N. N. Bogolyubov, January 21, 1955'

A A
TIKHONdV. A.N.. prof.; SOKOLOV, A.A.P. prof., otv.red.
[Program in higher mathematics; for the F17sics faculty] Programme
po, vysehei matematike (dlia fizicheskogo, fakuliteta). 1956. 7 p.
(MIU 11:3)
1. Moscow. Universitet. 2. Chlen-korreBpondent All SSSR (for
Tikhouov)
(Mathematics--Study and teaching)

Catogory :U"OSP..!TIIoor,.-ticaI Physics - Quantum 21cetrodynf-min-s B-5
..bs Tour :Rof Z'iur Fizi1m, 111o 3, 1957, No 5674
-luthor :4 Sokolov,0.Amp"p-
10 :'ITicory o.'L-.%G Pladiatinp- _'loctron
Orig J.-ub:Tr. 3-go Vscs. L.-Laterq. s"ozdi, 2. bl,, LN SSSR, 1956, 95-96
.,ostrac L:',f.c;r ciovoloping the thoory of tho cmissiun from a radirt'Un6
,jo.ptron, tho author, iiqurticular, not.--s the rosults obt-tinod
b intly vrith L,at-ioycv, th%t ubc attonuntion timc of
thn bc) Latron Osci-Ila-Gions is
whorc q is th.- 'Lrdux roprosont-ing tho drop in t1ij magnc%ic
ld ncar 'ho oquilibrium orbit -..-ith radius r. This timc
is largo oomparcd .7ith tho sonsiblo valucs of tho duration of
tho accolcration cyclo, and conscquontly, th~D mcdiaticftal
c-in bo nogloctod up to vci7-.- largo cm~rgics.
Card 1/1

N
RUMkNIA/Theoretical Physics B-5
Abs Jour Referat Zhur - Fizika, No 5, 1957, No 1086-9
Author Solk9lov, A.A.
Inst Moscow State University
Title Concerning the Problem of the Possibility of Excitation of
Macroscopic Oscillations by Quantum Fluctuations
("macroatom").
Orig Pub Bul. Inst. politehn. Iasi, 1956, 2, No 1-2, 39-42
Abstract The author considers the effect of radiation on the motion
of an electron in an axially symmetrical magnetic field.
It is shown that the presence of radiation leads to a chan-
ge in the radial quantum number, i.e., to an increase in
the square of the amplitude of the radial oscillations.
The author also gives a semi-classical interpretation of
this phenomenon. The author indicates that the motion of
Card 1/2

RUMAVIA/Theoretical Physics B-5
Abs Jour Referat Zhur - Fizika, No 5j 19571 1110 10869
the electron in an axially symmetrical magnetic field in
the presence of radial oscillations with macroscopic am-
plitudes forms some kind of a "macroatom". It is indica-
ted that a unique principle of uncertainty exists for the
"macroatom". It is emphasized that the quantum correc-
tions are first connected together on the radial oscilla-
tions -/ El/5 Gk -1/5), E,,_ ~ mc2
(E/mc2~ for energies E.
--"4j and then on the ax'i'al oscillations (at E
El/3)1 and finally, in the region of very high ener-cries
(at E ' El/2) -- on the radiation intensity.
Card 2/2

4-7.

Distr: .4930 /494c

'The theory of the
o
A; and j
_7_45
l
ft
ft 1411W
mass ir the presence of an external inedium.
tron
el
1
c
Soviet Ph~-Sic_-. JETP 3 (1956), ~4-97.
-
te the difference between ',lit: value of the
To calcula
electron mass in vacuo and in a medium chiiracterizEA by
its dielectric tht,
-constanx and its
nja~rtetic R~Url
_
field equations of uantum electrod in are solved
in second approximation ior I ie evilission and ah'sorption
of '.i pbuton in the niedium, A convergi-nt expression
obtained for this diffQrence and for the currespondinl,,
kvvl shift in a hydrogen atoin. This shift is much smailt-r
thim div Lamb sbift, hitt mick-r normal prussure and
h

-
'lijj)vlAtjLrt! tlKill tile Shift 11LIO U, Ow hit nicti
111--tweell Ow Cluctrull aild tilt- radimioll fivid. E. Gora.

USSR/Theoretical Ph3sics Quantum Electrodynamics. B-5
Abs Jour Referat Zhur - Fizika No 1, 1958, 191
Author Sakolov, A.A.
Inst ------------
Title Relativistic Motion of Electrons in a Magnetic Field
with Account of Quantum Effects.
Orig Pub Vestn. Mosk -un-taser. matem., mekhan., astron., fiz.,
khimii, 1956j;No 2, 27-46
Abstract An article of review character. The introduction discus-
ses the fundamental premises of quantum theory of the ra-
diating electron. The following chapters consider in de-
tail the swing of the betatron oscillations of electrons
in cyclic accelerators, due to the quantum character of
radiation. Problems connected with radiation damping of
betatron oscillations are briefly discussed in the appen-
dix.
1/1 4
Card

537.5
33.9
ON THE RADIATION EMITTED BY ULTRA-HIGH
VELOCITY ELECTRONS MOVING IN A coNsTANT mka-
NE171C FIELD. A-A.Sokolov and A.N.Maiveev.
g
Zh._Vkspvr_.tPor.4W=,TM-3U,_ No. 1, I2V3-5-(I956). In
Russian.
M
The present paper is a continuation of prevIous;
gations of the quantum theory of the I'luminnuall electron (see
preceding abstract). A formula for the differential radiation
spectrum W been obtained which Is uniformly correct in any
spectral range and for energies of the
E Esh. A closed formula for the total radiation energy
which is uniformly valid for arbitrary eneigies of the rAdla't-
Ing electron and also a formula for the "critical" radiation
frequency of the "luminous" electron have been obtained. A.

530.14,5
PRESENC 0 LM&-%IN TH
A ME IU E
Zh, ekspe r Fiz, 0 S -.I
teo 1. ANA 4LEY and yg~
.T,
RUB
"'Inid contributions 0 (19 5 6). 1 n
Ft.
Mediurn are cOnsidered.t' th' AIMPP Mass due to an external
06taken Int The e&ectron'
. account in the calculations. -.13081tron vacuurn is
Card
t ical 1y- -indepen-d ell t f-hic tiidtiori - rorces - in - Cue-
of the electron, The authors interpret the identity of both methods as a con-

Zurn.eksp. i teor.fis, ~O, 802-803 (1956) CARD 2 / 2 PA - 1226
nection between the quantum-like method and the theory of oscillations where
the so-called MARKOV chains occur, i.e. the statistical independence of suc-
cessive processes,
The authors endea~7or to explain the quantum-like micro motion of the electron
by the effect produced by fluctuations of virtual photons~ Under the influence
of the field of virtual photons the classical quantities x and px (momentum of
the particle) become non-commutating operators, and in first approximation the
same exchange relations as in the wave theory are obtained. If, for x and p x
the corresponding operator expressions are put, the energy levels for the har-
monic oscillator are obtained. If a certain formula for the momentum is used,
zero energy automatically contains the necessary terms of subtraction, and the
f ini te quantity E0 . -h w /2) + 2e2/31,c3m)(ln(3c3m/2e 2(1 )-1) remains.
0 0 0
The first term Js the known expression for zero energy without vacuum terms,
and the second term is due to the influence of the vacuum. Similarity to the
corresponding strictly quantum-electrodynamically derived formula is shown.
Thus, the classicAl motion of an electron itself becomes quantumlike by inter-
action with the secondarily quantized field of the (really emitted or only
virtual) photons.
INSTITUTION: Moscow State University.
SUBJECT UbbR / PHYSIC3 WD 1 / 2 PA 1660
AUTHOR 60KOLOV, A.A., TERNOV, I.M., 5TRACHOVbKIJ, G.M. ons in
TITU fhe -Investigation of the Stability of the Motion of u Electr
Cyclical Acceleration devices in consideration of Q antum Effects-
PhRIODICAL ~urn.eksp.i teor.-fis,31, fasc-3, 439 - 448(1956)
Issued: 12 / 1956
In connection wLt,11 this quantum-theoretical investigation of the motion Of the
electron in a magnetic field thd possible occurrence of radial and also of axial
oscillations is taken into account. Such problems are best Solved in cylindrical
coordinates r, z,1P.
Above all the motion in cylindrical betatron-like devices is explained, in which the
magnetic field H is modified within the domain of the stationary orbit (r=Ro-const,
H = cons,t.r-q. The mean value H is assumed to satisfy
z=0) according to the law R d further be it assumed
the WIDER04 condition (2/R*) o.rH(r) dr = 2H(R 0) an
that div H.= 0 and curl 09 0. , f0 are investigated. The
At first the adiabetic invariants and the equilibrium orbit rld an
electron orbit taking-quantum effects into account can be dete ined by me s of
~OHWs theory, and resulLs in first approximation agree with those of the rigorous
quantum theory. This mAhod is well suited for practical purposes- Here three adia-
betic invariants are introduced which are in connection with the azimuthalj radial,
and axial quantum m. "embers. the present equilibrium orbit are in-
Next, the oscillations of the electron round casion the adiabetic in-
vestigated on the basis of the classical th6ory. on this oc
ariants are supposed to be different from zero. The quantum-like c Iorrections to

SUBJECT USSR / PHYSICS CARD 1 / 2 PA - 1663
AUTHOR SOKOLOV,A.A., TERNOV,I.M.
TITLE On t e Pola-r-ization Effects in t-he Radiation of the Radiating
Electron.
PERIODICAL gurn.eksp.i teor.fis,31, fasc-3, 473-478 (1956)
Issued. 12 / 1956
These polarization effects are investigated by quantumlike methods, but in
classical approximation. At first the amplitudes of the linear and circular
.polarization of the photon field are computed. The commutation relations for
the amplitudes of the vector field are given. On the occasion of the investi---,
gation of the polarization effect it is necessary to subdivide the amplitude a
of the vector potential into components, each of which characterizes a certain
polarization state. In the case of linear polarization a must be subdivided
into two components which are vertical to each other. Also the procedure to be
applied in the case of circular polarization is mentioned. The expression for
the radiation intensity is W i . L (I dQ sin 0 Wi(y Q), and on this occasion
2 V 0
the relation Wi(1r,Q)- ce Si applies to the spectral- and angular distribution
of radiation intensity. The index i characterizes the polarization state
(i - 2,3,1,-l) and 9 denotes the angle between the wave vector and the
z-axis. Also a formula for the connection between S and the amplitudes of the
photon field is given. The expressions for S are specialized for linear and

Did.. CONTMOUTION TO THE OF
PARTICLES BY A FWD CENTRE (Or FMCEJ WrM DAUPLPM
TAUNUMACCOUNT. A.A.MkolovandSAXerlmov. , ( PA r1
Zh. ditaper. teor. Via, V077-NMfIft, 060-11556). in flumd n.
Expreseloos for phxce-shut an4 (or dittarential, cross - secti:
are given 16 accoitiance with a theory- in wbIcb d2wplfia Is taken
into account. Theme expressions are xpplied to "rectangular"
poWntial and to a a-function type of potential, both In three dimensions,
The results aro coo,.pAred with thaso obtained by alternative
rauthods of calcul2tion. R-MI-L"chl
AL

SUBJECT USSR PHYSICS WD 1 / 2 PA - 1979
AUTHOR SOKOLOV,A.A., IVAKENXO,D.D., TERNOV,I.M.
TITLE. On the Excitation of Macroscopic Oscillations by Quantumlike
Fluctuations.
PERIODICAL Dokl.Akad.Nauk ill, fasc.2, 334-337 (1956)
Issued: I / 1957
The energy of a relativistic electron moving in a homogeneous magnetic field H
can be represented as the sum of the energy of the rotation movement E 1 of the
electron and the enp1gy of the oscillation motion E along the radius:
--I s
E 2eHc'~ 1 + m2049 Es - d a E(V 2a2/2c 2. Here n = 1 + s denotes the
principal quantum number, 1 the azimuthal- and s - the radial quantum number,
a - the amplitude of the radial oscillations. Next, formulae for the modifica-
tion of the rotation- and oscillation energy on the occasion of the transition
of an electron from the state n into the state n' - n - Ir is given. The sum
of these two modifications results in the entire energy loss by radiation while
taking account of quantumlike corrections with an accuracy of up to '~ .
The quantumlike corrections to the rotation movement can take effect only in
the case of high energies. With t -4 0 there is no modification of the energy
of the radial oscillations at all, i.e. in the classical case the value of s
remains constant even if radiation is taken into account. Only in the quantum-
like case ( ~ - 0) does one peculiar energy jump occur if rotation energy is
used not only for radiation but also for the excitation of radial oscillations

~: r : - ~ ~ -; I
~,.C! Ulal T-S 5-' Cercetrri
c
3, July/sept.iq-~,
-lily I ii cix f c 7.~ rc,-,e,,n ~ccessicrls Lr. Ycl. 7, nc 2,
e b r r,

di
- - - - - - -- ------------ -------------------------------- ---------------
c i4a- R Sq: I
Aa
at
r 4(e4il~4
I rg by
"Cow t1he scalcor
a~d for ;b~~ ph'-s
-j formallas C, L.!.! ILA I,".' J ! i

90NOLOV, A.A.
"On the Theory of the ,Luminous' Electrons," paper presented at
CERN Symposium, 1956, appearing in Nuclear Instruments, No. 1. p . 21-30,
1957

I
I
I
~l
I

AU
A THOR, SOKOLOV A A., KERIMOV,B,K. PA - 2007
TITLE: _~n~ heory of the Scattering of Particles by a Steady
Center in Consideration of Damping.
PERIODICAL: Zhurnal Eksperimentallnoi i Teoret.Fiziki, 1957, Vol 31, Nr 6,
pp 1080-1081 (U.S.S.R.)
Received: 1 / 1957 Reviewed: 3 / 1957
ABSTRACT: The theory of damping proves to be the stage that follows accord-
ing to the perturbation theory and allows the calculation of the cross section
a not only within range of the long DE BROGLIE wave lengths (a 0 2), but also
within the range of smaller wave lengths (d '~/~2). The relation C+C+ ~ C1+01-1
set up in connection with the development of the theory of damping k' indi-
cates that the total sum of the inciding and scattering particles stays constant
at any moment. Scme preparatory works on this matter are cited.
At first the exact formula for the cross section of the elastic scattering of
2 2
particles with the momentum t k(k=2n/A ) is given: Li;-(Wk ) T= 0(21+1)sin
The perturbation theory allows the determination of the phase of ~ I in the
case of '~1 P . It is shown that one can
define a function q)' P3(P such that:
(E' - c(a P-') 93 MO 02) (P I =Z 0
From this point on the discussion is concentrated on the longi-
tudinal component of the vector equation, that is to say the
component in the-propagation direction. The properties of
the longitudinal component of ~' are compared in some detail
with those of the original ~ for various Dirac particles
(neutrimosl electrons, etc.) having various spins. A polari-
zation vector for the longitudinal component is defined, and
shown formally to obey the same matrix operator rules as the
E!-i-n -7;-e-.torS. The contact transformation from q)* to q)
does not in general leave parity unchanged; in fact it can be
shown that parity conservation, if it occurs, must be accom-
panied by selection rules on the polarization operator. How-
ever, time reversal and change conservation, as would be ex-
Card 2/3 pected, give no additional restrictions. A section of the

SOV/139-58-5-34/35
Longitudinal Polarization of Dirac Particles and Parity Non-
Conservation
paper is devoted to the explicit formulation of the 'longitud-
inal spin' operators for neutrino and antineutrino. The paper
contains no figures or tables; there are 12 references, of
which 1 is German, 1 Soviet, 1 Italian, 9 English.
ASSOCIATION: Moskovskiy ordena Lenina gosuniversitet imeni M. V.
Lomonosova (Order of Lenin State University of Moscow imeni
M. V. Lomonosov)
SUBMITTED: June 4, 1958.
Card 3/3

SOKOLOV, A. A. Y B. K. and GUSEYNOV, 1. 1.
"Damping Theory Study of Elastic Scattering of Dirac Particles with Account of
Polarization Effects," Nuclear Physics, Vol. 5, No. 2, Jan 1958 (North Halland
Publ. Co., Amsterdam)
Physics Dept, Moscow State Univ, Moscow, USSSR
Abst. Elastic scattering of Dirac particles by a short-range force centre is
considered from the standpoint of radiation damping theory. The expression for the
scattering amplitude is determined. The inteigral equation thus obtained for the
scattering amplitude permits one to investigate polarization effects.

56-1-17/56
AUTHORS: Sokolov, A.-A. Guseynov, 1. 1. , Kerigov, 3. K.-
TITLE2 On the Scattering of Dirac Particles by a Short Ra-nae Force
Centre According to the Damping Theory (K rasseyan-iyu
dirakovakikh chastits korotkodeystvuyuahchim silovym tsentrom
s uchetom zatukhaniya)
PERIODICAL: Zhurnal Eksperimentallnoy i Teareticheskoy Fiziki, 1956,
Vol. 34, 1[r 1, PP- 110 - 112 (USUR)
ABSTRACT: In the present work the elastic scattering of Dirac particles
by any short range force centre is investigated according to
the damping theory. The wave functions are subdivided here
according to the value of the projection of the spin onto the
Z-axis (M = + 1/2) and not according to the value of proJec-
tion of tRe s-pin onto the direction of motion. The intearal
equation for this case is written down explicitly. A formula
is also given for the matrix elements of the transitions on
which occasion the spin proportion of the matrix element is
given still more precisely. Moreover, the authors use various
Card 1/2 recurrence formulae. The expressions for the components of

56-1-17/56
On the Scatterin~~ of Dirac Particles by a Short Range Force Centre Accord-
ing to the Daap4-n,- Theory
the matrix element obtained after some further trangformationscn
written dorm. It is possible to produce the orthoE~onal charac-
ter of the matrix elements necessary for the damping theory.
The thus found differential cross section of the elastic scat-
tering and an expreasion for the amplitude of scattering are
given. Concluding, the total cross section of the elastic
scattering is Yrritten down. There is 1 reference, which is
Slavic.
ASSOCIATION: Moa6ev State Yh&MYSIty
Odoskovskiy gosudarstvennyy universitet)
SUB.P.-UTTEDt J111Y 10, 1957
AVAILABLE: Library of Congress
Card 2/2

AUTHORS,1 Sokola~,~ A,_A____Loskuzo-.-'Yu. M. 56-34-4-47/60
TITLE; On the Cherenkov Radiation of, Longitudinal Polarized
Electiona (0 cherenkwrskom lzluchenii prodolvno poiyari-
zo;rannykh elektroncor)
PEaIODICAL" Zhurnal eksperimeritallnoy i teoreticheakoy fiziki: 1958~
Vol. 34, Nr 4. pp. -:022-i023 (USSR)
ABSTRACT! The p-lesent paper generalizes the results of a pre,.rious
paper by the same author (Ref 3) dealing with the polari-
zation propertiei of Cherenkov radiation for the case of
icngit,udina, poiarized electrons. For their calculazions
the authors used vaiious formulae given in the book by A. A.
Sc,kolov and D. D. Ivaneako I.Ref 0.
Cherenk~-.r radiation will c-onsist, of three parts"
w Max Wmax
2,
ZiA A
W
quanfleed long.'.,. tudi-Mai

On the Cherarikov Radfation of Longitudinal Polarized 56-34-4-47/60
Electrons
7,11 Pre ((J.,~ - ti ( I - C. 20) denotes the (completely
'k '_
linearly polarized) classical part of the radiation;
2f,- 3, 2 2 2,
quantumlike- tj / 2 P n" the completely
unpolarized quantumlike additional term;
IT ((,)*] - .. (-/~n)cos 0) character-
longitudin-al /% %,
ize,q the long-Itud-inal polarization of the photons. It is
interesting that this part of the radiation is pro-
po:rtiondi not to f. but to k2 . The following formula holds
for the degree of circular polarizations
P Z. I . 1. 1 1. =
:w., ((jl - w,, + w,,.,
There are 4 references~ 4 of which are Soviet.
ASSOCIAT121i Aloskovskfy gosudarst-ennyy universitet (bloscow State
University"
SUBMITTEDs JanDary 16, 1956
Card 2/3

'I sov/56-34-5-59/161
AUTHORS: '50.Kolov, A k Lysov, B. 1_
3 of Longitlj.dinallY poi&rlzed PhOtOns On Elec-
TITLE: Compton Scatterini
t-!,ons with Oriented S- onovskove rasseyanive prodollno
pin (Kompt
poly,-.r'Lzo1r-_nnykh f0tonov ra elektroria.Kn s ori-yentirovannym, spinor-)
PERIODIC'U': Zhurael ci-six,~rimenl:al`noy i teoreticheskOY fizikl~ 19519.,
Vol. 34, Nr 5, pp 1551-1351t (USSR)
ABSTRACT: In connection with the discovery of the nor,- conse r-ration of Parity
the further development of quentum-ellectrodylaamics of electrons
and photons with a longitudinal polariz-, tion is becoming a prob-
lem of topicEa interest. To cd_-nsider th-e long-itud�ne-1 polariza-
tion of the electrons in the computation of the mr-trix elements,
not 'bhe forrmls. by Casimir (liazimir) but. the foiuula (21,12)
from the book by A.A. Sdsclov *x-d D.D. Ivwrienko (Ref ~) has to
be used, s denoting tte eigenvaLlue of tbe opera; .or
A - , This Operator describes the double projection
2
of the eleatron spin upon its dire,:tion of motion. This formufLa
c.g.r- be used in cases where the electron ir_Ltially IS a;'- rest.
For this case the forwal.a Is vritten down explicitay. Then an.
expression for the covresDonding mr-_',.r,Lx- element. is giver-, From
Card 11/3 these express:.ons a genera lization of the forrofia. by 1(leiri.-Nisbina
SO-7/56-34-5-59/61
ed FllotO--s on ElectrcL's
f Lono tU&i11--1-:-Y Fc'~!~Z'z
Coluptoa sc~tteririg 0
,ith oriented Spirl d Startir-6 vlth these ey-PressiO-as the formala.
11 y, -be der:~ve t."he Jri+':La'~.'spin of
(Kleyn Q C13 'zc tbr,,t case ~jjie~e 12 -1 r
-NishirA I)j_a States
by r-ekn-Visbi~rJA C, be generaLL where the - + the orienta-
t'~-e orien7t&tiOrl
the electr~'a 12E-5 - ~.--r-polarize&
terix--g of a 0- 1 law Of
are sume& UP- sce.t luen-,e jjp!:r_ "he :L-ategr& S c all izat'ior, of
of the spi-_ ras no. A-af r9J.-:P of the polar
tion t-;C,-n of +'b.r-- ase tb-ere is
I - .." nnu-re lxi -
a for the COMFj-r-'~- lat . -Stic c
A. fOrMLI-i- S~t I " V -_ 9. 0 the u-,
1-ra
the scat,,te:red ra 2 '_.oS + Cos-
L_ ~.4.!r. st-iv e ,f -vride scat"erl-'ng
,Dbt-ad-,-e& Pn_.:~,are: 0-_q i_r. +tie cas - the prob-
v-istic case The Scattere ay,i7 A jr.-Verse problem to
"vC -ed S _.
be cliCula--ri-Y _,;_ on Of langitudi_n5a-l'y
T.d~r'-aa:u ;..; I
e t7jo_photo~~' is
lem iavestiv--ted abcr'Te th qt iest I-rit-'l a ga-vea sPill
polarized PDsitrOL' ()~" electrons -esporldinC v0s. sectioa
expYession for tAle COT'l .baa. as-.Ymetry exist..
discussed. AU j,&j-,ior~ and. 0,11 Kzilml-~, P-Jsitrons
case a 7-op_ti'~al Of the
pho - c -
In the ex tVO_1 tQ-0, ELnn�'-~:
~~le 0 aPP-Ly Ui kietermi
This Makes POE'S ..e. e)Lpe_,Tir1er, siP;tion O'r legre~
0,-ente(i eiectr0r--s t
Card 2/5

SOV/56-31,-5-59/161
Compton r3catterling of Longitudinal-' y Polarized Photons on Elec trolm
wit-h Oriented Sp--'-.
of IC;.qIr7It"akftLYQ. polarization of positrons. There are 6 references, 4
of which qxe Soviet.
ASSOCIATIOIT: Moskovskj.y gosudarstvennyy universitet (Moscow State
University)
Sb-BiLIMED: February 27, 1958
1, Photons--Scattering 2. Electrons--Properties 3. Nuclear
spins 4. Mathematics-4pplications
Card 3/3

SCV/20-122-5-1/56

o~ad Sol-OlOVY
M. A.A.

0-rTS a Function
6101, for Cmetricbes-
5
zhdenn
YrO
' a~Laealye dlYa Ir. oY giperge
c
A,o IT
P 751-754 (USSR)
'
r
"d,
SSISR, 19 53, 1 5, P
Lutions of a
O
0 f
r
Pto~,*~12 D4haviL
F
85q3
~h
.
he S
. _
es
for"n
of -the

i )
ts + -(-
u 1'ation of equatiOll
Va e 80
aws
I t~e foM

2)
4
(2) in
_111vactiMs. ._jttig
S,,LS--,,i
z
c
- (Z)
35
lz1z.,P S

Go
"Ic for t'--3 Decentmabe~i SOV/20-122-5-1/56
,-me Z(21 are two linea.-!ly independent solu-
S
Of "t equation aml L emd B exe cmztants. The results
cy exiti-ior 2- -.;7ae locatioa of asym-ptot a for-M12AS
U0
c:.- S ile;~ene:-Mte LFqe~, geom tric functian W f6 IL(x) and to
nuc~-, cas-zm o,., -b:-14-s f~,;ic-bion as Hermit-'.au and LAguerre
UlA !Xmsel Amclu'lon., and also to the derivation
o: fo::-,2m2a. Mere Pare referene-asp 4 f c a
o vhi h re
unive.-mi'"'et imeai M.V. Lawmmso-ua
imen: Lcmo---oov)
Zkme 2, V-13 by 23ogolyubmr, Acadeifef'..c.2
C 2/-2

P'.'ASE I BOOK EXPOITATIO!q- SOV/3905
Filosofskiye voprosy yestestvoznaniya, [sbornik] II: Nekotoryye
filosofsko-teoreticheskiye voprosy fiziki, matematiki i khimii
(Philosophic Problems of Natural Science, (Collection of Articles)
II: Philosophid and Theoretical Problems of Physics, Mathematics,
and Chemistry) [Moscow] Izd-vo Mosk. univ-ta, 1959. 248 p.
Errata slip inserted. 8,000 copies printed.
Editorial Board: K.A. Rybnikov, Kh.M. Fataliyev, and M.I. Shakhparonov;
Eds.: R.A. Aronov, and A.A. Konoplyankin; Tech. Ed.: M.S. Yermakov.
PURPOSE: This book is intended for scientists interested in the history
and philosophy of mathematics, physics, and chemistry.
COVERAM This is a second collection of articles prepared by the staff
ofthe Department of Dialectical Materialism of the Moscow State
University. The first collection was concerned with.philosophical
problems of the biological sciences, specifically Michurin's theories.
The present collection consists of 14 articles divided by fields:
physics, mathematics, and chemistry. The collection commemorates
Card 1/4

SOKOLOV, ,,. A.
"Theoi-j of Dirac Particles with Oriented Spius arid Parity Non-Couservation"
Nuclear Physics, 9, No. 3, Jar-,. 1959, 420-425 (North Holland Publishing Co., Amsterdam)
Abstract: The Viders-Pauli theorem is investigated in connection with a type of theory
chosen to describe Dirac particles with oriented spins.
Moscow State University

66603
SOV/139-59-3-20/29
AUTHORS: Sokolov, A.A., and Loskutov, Yu.M.
TITLE: On the Theory of Bosons and Fermions with Oriented Spin
PERIODICAL; Izvestiya -,rysshikh uchebnykh. zavedeniy, Fizika,,
1959, Nr 3, pp 132-142 (USSR)
ABSTRACT: Lee and Yang (Ref 1) have predicted that in the case of
weak interactions parity is not conserved. In phenomena
involving the neutrino (fermions with zero rest mass)
the nonconservation of parity may be explained with the
aid of the two-component theory, or with the aid of the
theory of Dirac particles with oriented spin (Refs 27 3).
In the latter case7 and for positive energies (c = 1~
neutrino), it is necessary to retain the solution with
one spin direction (8 - S), and for negative energies
(s = -17 antineutrinos with the other (S-1 = -S). This
may be achieved if the wave function W satisfies both
the Dirac equation and the additional condition given by
Eq (1) (Ref 4), or 0, - el) - 0 where W = ej Se = I
aly -6 = -1. The quantity
(or -1) both for e = 1 n
Card S6 = S-c is proportional to the projection of spin onto
1/2 the direction of the momentum p. In the present pape'r
an attempt is made to generalize this result to particles

A7THORS: Sokolov, A. A., Muradyan, R. M.
i F_ 22 _." k -.
TITLE: Developmrit of the WKB Method of Approximation\~,
PERIODICAL: Vestnik Moskovskogo universiteta.
astronomii, fizikip khimii, 1959,
S/055,/59/000/04/006/026
BO14/BOO5
Seriya matematiki, mekhaniki,
Nr 4, pp 61 - 78 (USSR)
ABSTRACT: In mathematical physics, special functions which are exact solutions
of differential equations are often approximated by-simpler func-
tions. The authors mention'the method by Liouville-Steklov (Ref 1y
for differential equations of second order, and then explain the
method of approximation suggested by Wentzel, Kramers and Brillouin
(Ref 3) (WKB method) for the solution of the wave equation. In this
method, already the first approximation gives good results. In the
present paper, this method is put forward in a generalized form.
Besides, better approximated solutions are derived for a number of
cases by finding the solution of a differential equation "neigh-
boring" the original differential equation. In the first principal
part of the present paper, the solutions (2,11) and (2t12) are
obtained by the M method starting from the linear differential
Card I/ equation of second order ull + f(x)u - 0 (2,2). The first solution

68870
'99-46-00 S/139/59/000/05/012/026
903 2/Ell1+
AUTHORS: Sokolov, A.A., Ternov, I.M., and_Loskutov, Yu.M,-
TITLE: 6i the 1 -- ---- -- ~P--- tion Properties of the_�Ri
rans orma _jn/~
Pseudovector
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy, Fizikaj
1959, Nr 5, pp 72-80 (USSR)
ABSTRACT: Problems connected with the spin properties of particles
have recently become more important in view of the
discovery of the non-conservation of parity (Ref 1).
The present paper introduces the 4-vector of polarisation
of Dirac particles by a covariant method and investigates
its transformation properties. The transformation law is
shown to be of the form given by Eqs (11+a-2). The
results obtained from an analysis of the transformation
properties are used in connection with phenomena in which
parity is not conserved, In particular the Xpe decay
is discussed and it is shown that in the laboratory
system, the spin of the p meson makes an angle a with
the direction of its momentum which is given by Eq (21),
Card where ~,~ is the angle of emission of the V meson.
1/3 The appearance of a transverse component of the Ii meson
spin in the laboratory system has also been considered by

68870
S/139/59/000/05/012/026
B03 2/Elll+
On the Transformation Properties of the Spin Pseudovector
Ascoli (Ref 9) but differs from Eq (21) by the factor
given by Eq (23), which takes into account relativistic
contraction of the transverse components of the'spin.
In fact, the axial spin vector characterises the
circular polarisation in the pldne perpendicular to its
direction. For the longitudinal spin component this
plane is perpendicular to the velocity of the particle
and hence the polarisation remains unaltered. In the
case of the transverse component, on the other hand, the
velocity vector will lie in this plane and hence the
polarisation will change. For particles with zero rest
mass, the angle a vanishes, i.e. if the axial vector
.a is parallel to the momentum vector _% in the given
inertial frame, they will remain parallel in all other
inertial frames. This can be used to characterise the
neutrino and the anti-neutrino by different values of s,
namely s = - 1 and s = +1. If the polarisation of
Card the neutrino is characterised by its helicity, i.e. by
2/3 the rotation of the component of the vector g4) which
is perpendicular to the momentum, then in transforming

3/055 59~000/06/07/027
B 06X00
AUTHORS: \,9okolov, 1. A., Muradyan, R. K., Arutyunyan, V. N.
TITLE: Development of an Approximate WKB Method
PERIODICAL: Vestnik Moskovskogo universitsta. Seriya matematiki, nekhaniki,
astronomii, fiziki, khimii, 19591 No. 6, pp. 64 - 86
TEXT: The present paper continues the first part published in "Vestnik Noskov-
skogo universiteta", 1959, No. 4, p. 61. It begins with j 4 dealing with the
confluent hypergeometric function and deals at first with the Whittaker func-
tion. The formulas derived are subsequently applied to a concrete case: the in-
vestigation of the emission of an electron moving at ultrarelativistic velocity
in a constant, homogeneous magnetic field. The problem is schematically shown
by Fig. 1; Fig. 2 shows the dependence of radiation intensity on the number of
harmonies. The subsequent chapters deal with the Laguerre and Hermite poly-
nomials, the quantum correction in the theory of "radiating" electrons, and the
determination of eigenvalues (the approximate method developed here does not
only permit a derivation of asymptotic expressions for wave functions but also
a determination of eigenvalues of the parameter X - cf. Part I). The paper
Card 1/2

I
Development of an Approximate VrKB Method
8/055~59/ooo/o6/07/027
B006/BOO5
concludes with a comparison of the asymytotic formulas with the accurate for-
mulas within the range of relatively small quantum numbers. (Abstracter's Note:
Without knowing the first part of the paper it is not possible to follow the
course of calculation, all the more so as all definitions necessary are missing.)
There are 5 figures and 11 references, 9 of which are Soviet.
ASSOCIATION: Kafedra statisticheskoy fiziki i mekhaniki (Chair of Statistical
Physics and Mechanics)
SUBMITTED: April 9, 1959
Card 2/2

SOXOLOV, A.A.; MURADY&N, R.M.; ARUTYUNY-Ul, V.M.
Development of the approximate method of dentzel. KramerB, and
Brillouin. Vest.Xoek.un.Ser.mat.p mekh.,astronffiz.~chim. 14
no.1t:61-78 159. (HIRA 13:~)
1. Kafedra statisticheskoy fiziki i mekhaniki Moskovskogo
univerBiteta.
(Approximate computation)

24 ( 5) V.,, -2 _ 7 7
~7/

THORS:
U
Sokolov, A. A. , ;'rutyunytn, 7. 7;. , 'Luradyan, R.
I -
TITLE: The Calculation of the Phases of 'Scatterin,-,- Taking fftDA-,:~oun~,
("he Second Approxim-tion (Vychisleniye fa7 rasseyaniya s
uchetom. vtorogo priblizheniya)
PERIODICAL: Zhurnal eksperiment_~llnoy i teoreticheskoy fiziki, 10,50.,
Vol 30", Nr 2, PP 594 - 590 (USSR)
ABSTRACT: In the present paper the authors calculate the phase shifts
of the elastic scattering of Dirac (Dirak) particles in
second approxime-tion with respect to the interaction poten-
tial. An exnresoion is given for the general solution of the
free Dirac equation of this problem. This solution is not
li-nited by a condition of finiteness in the origin of coordi-
nates. This solution of t';,,e free equation is also an asynpto-
tic expression for the Dirac equation if there exists a
spherically symmetric short-range force center. The next
part of the paper gives an approximate solution of the Dirac
equation for the case of a centrL1 field. An intel-r--l equation
Card 1/3 equivalent to the Dirac equation is given for the case in

The Calculation of the Phases of Scat terinJ Taking SOV/56-306-2-37/63
into Account the Second Approximation
which there is no vector potential and the scalar potential
is spherically symmetric, The interaction energy is considered
as a pertifttion and the calculations are carried out in
second approximation; the wave function corresponding to
this approximation is given explicitly. The calculations
are discussed step by steD and the expressions found for
the phase shifts are given explicitly. Neglecting the terms
which are square with respect to V(r), one obtains the
same results as in the theory of damping for the scatterin.-
of Dirac particles. For small values of the scattering phases,
the results of the first Bornkpproximation are obtained. The
results of this paper may be used also for the investigation
of the scattering by a Coulomb (Kulon) center,(V(r)=_Ze2/r).
The inte.-ral values of the phase shifts diverge in this case,
but correct results are nevertheless found. Finally, ex-
pressions are given for the scattering amplitudes (in second
approximation) and for the differential cross section. There
are 4 references, 2 of which are Soviet.
Card 2/3

Thp of t'.it-- of Ta I -. inF, fS--; V 3
into Account tn-c Second ~-ltion
.30C IO'T: 1jo.-kov-',-Jv uriiv:,-r,,-itet
'S" .;, - - (,..o cow ~t-t- Unive.-
A
SUB!.'.TTTI?,I): .o!Cufit 26, 1950
Card 3/13

24 (5 SOV156-36-3-i.-6 /71-
AUTHORS: Sokolov, A. A., Ternov, I. M., Loskutov, Yu. Y'.
------------
TI TLE - On the Problem of the Covariant Determination of t%e Spin
Pseudovector (K voprosu o kovariantnom opredelenii psevdo-
vektora spina)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fizjki, 195~,
Vol 36, Nr 3, pp 930-932 (USSR)
.ABSTRACT: The present paper ("Letter to the Editor") is based upor. an
earlier paper by Sokolov (Refs 1-3). It has already been shown
that the longitudinal polarization of free Dirac particles
U t;~
can be described by the operator j/k. This operator occurs
as integral of motion with the ei:gen value The authors
endeavor to connect with the value.ft" , not only longitudinal
polarization but also transversal polarization as ~-;ell as the
time component of the spin vector. Proceeding from the ,,;ave
function for positive energy in consideration of the spin
state equations are derived for the components of the spin
vector. The transversal and the time component, which do not.
occur as integrals of motion, can be represented as mean value
Card 1/2 KS*'6-,Pd 3x, K = k / V 1 7l.
o

SOV/56-36-3-48/71
On the Problem of the Covariant Determination of the Spin-pseudovector
It further hoLds that
c 0 s k 1-S3, sin 8,
1 k0 V 1-S 2 =
~3 ks, ~4 = iks; several special cases are investigated.
There are 7 references, 6 of which are Soviet.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet (hioscow state
University)
SUBMITTED: October 27, 1958
Card 2/2

S/139/6o/ooo/oo6/026/032
E032/E414
AUTHORS- So Ing Professor of Moscow State University,
Stalin Prizewinner, Doctor, of Physico-Mathematical
Sciences, Voroblyev, G,A., Docent and
Moskalev~ V,A.-., Docent
TITLE- On the 50th Anniversary of the Birthday of
Alek"ndr Akimovich Voroblvev
PERIODrCAL Izvestiya vysshikh uchebnykh zav*d*niy, Fizikav
1960, No-.6, pp,,161-164
TEXT,-, A-A,Veroblyev was born in 1909, He attended the Tomsk
State Univ-ersity between 1927 and 1931, In 1931, he graduated
from the Division of Physics and Mechanics, In 1935, he
produced a "brilliant dissertation" and became a senior scientific
worker and Docent of the Tomsk State University in the
Department of Experimental Physics, In 1936, A,.A.Voroblyev
organized the High-Voltage Laboratory at the Siberian
Phyiitotechnical Institute and became its head, In 1939~ he
..*uccessful.ly completed a dissertation submitted for the degree
Ca a- d 1/ 5

S/139/6o/ooo/oo6/o26/o32
E032/E4i4
On tha 50th Anniversary of the Birthday of
A I eksiondr- Ak i xncP-,,- ich Vorob 'yev
d,evc-lopment of new A-ccelerator in6tallations, including a new
*at.,eguide acce1erator suggested by Voroblyev which wiii be
-capab;E- of producing '-ery high energy electrons, although the
c,~-vriill dimensicins of the -installation and the high-frequen:-y-
pow:er consumption will be small.., Re~sults obtained in this
w-f~.rt- reported by Vorob~yev at the International
Cc-nier,.4tice on Hxgh Energy A,-,celerators whi-ch was held in Geneva
in 1959. In the flfties~ Professor Vorob"yev also d1rstcted the
R,,esear~ch in he physa----~ of' solid dielectricmi Among Professr
Vojob'ye-'s publizations are.: "Charged parti~c-le atcel*rator.!:
"Eliei-trizal sir-ength of solad dielectrics"... MR i gh-vol t& g-t
,t e, bno I og y," ~"Ultra-high volt-ages," and othez monographa!
Professor Voyoblyev is the author of some 200 scientifit paper-j5
and 7 monographs and textbooks., He is a member of the Communz6t
Party of the Soviet Union (since 1940) and has frequently been
elect*-d as a mtmber of the local committe,w25 of the KPSU,
Irn 1959, the ---itiLisans of Tomsk unanimously elected h1m as thext
;a:d 4/5