SCIENTIFIC ABSTRACT SHAPIRO, I.S. - SHAPIRO, I.S.

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• Document Creation Date: November 2, 2016
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• Sequence Number: 8
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

�npiro, 1. S.- On transformation properties of wave func-
tions of particles with spin 112. Akad. Nauk SS-SR.
briial U-sper. Teoret. Fiz. 23, 412-416 (19.52). (Rus-1
Mathematiw-d ReviewS siall)
Vol. 14 No- 10 1 Indcra rhange of sign of the timeroordinate, it is possible:
Nov. 1953 to transform the fmir components of the Dirac wave furic-
Mathematical Physics *dml ill different. ways so that the sign of either the energy,
or the rharge changes. Theatithor discusses the meaning of,
Slich a "time reflection". The transformation under which!
the sign of the charge changes is non-linear. However, L.,
I lif,delill'i i'll [Physical Rev. (2) 82, 100 (1951); thcs~-Rev.'
12, 658] has brought about linearity in the field-freNase,
by inlrodiwing an eight-cornponent wave function whNII:
~atisfics :1 tgencrMization of the Dirac equation. Accordin'
to dic mithor, this procedure fails if a field is present. 1-1
Iliviefore proposes a generalization involving a qix-dinien-:
Sioll:11 Spare. N. Roscn (Flaifa)..

USSR/Nuclear Physics - Isotopic triplet FD-803
Card 1/1 Pub. 146-16/21
Author : Shapiro, I. S.
Title : The nature of 1-L- -mesons and Vo - particles
2
Periodical : Zhur. eksp. i teor. fiz., 27, 257-258, Aug 1954
Abstract : Letter to the editor analyzes the question whetherrEf mesons and
Vo particles form an isotopic triplet. Obtains affirmative answer
2
in the case where both particles are of vector type. Three references
including 2 foreign.
Institution : Moscow State University
Submitted : May 22, 1954

VDIsIntegntion on particles vrith a null mass at Mt.
1. S. Shapiro (Moscow State U:2iv.). ZhUF* Ekspd. i
3P3-7(l954).--&IectJon mles were obtained
for the d1sintegration of partlclc3 on 2 particles with arbi-
trary -Vln, if at least one of these posmses a null mass at
,rcq& Werner JacobsolL,
cap "m

USSRI Physics Quantum mechanics
Card 1/1 Pub. 118 - 2/15
Authors ShaT)iro, I. S.
Title Properties of symmetry- in the theory of elementary particles and nuclear
processes
Periodical Usp. fiz. nauk 53/1, 7 - 68, May 1954
Abstract Properties of symmetry, used in the theory of elementary particles and
nuclear processes, are described. Wo types of symmitry are considered.-
an exact and real one; and, an inexact and nroblematical one. The sym-
metry of the normal space (spatial symmetry) and the symmetry of charges
(charge symmetry) belong to the former-and the symmetry in the space of
an isotopic spin to the latten Sixty two references. Tables; diagrams.'
Institution
Submitted

x 7P1

U S S R
I-o-11tadiativa X-capture for forbidden transitions., V. V
Turovtsey and 1. S.
�ha tro (M. V. Lomonosay State Univ.:
_
Moscow). Do y Nauk S.S.S.R. 95, 777-0
(1054)~Morrlson and Schiff (C.A. 34, 5Z403) have given a
theory of radiative X-capture for permitted transitions.
T. and S. developed an analogous theory for forbidden
transitions of 1st order for the vector and tensor form of the
theory of 6-demy. Fcxmulas am givea for the ener,
distribution in the continuous -rspectium which resug
from radiative K-mpture. Since the Bc tion
-
y
.1
Is used, the formula3 apply to light nuclei
r

SHAPIRO I.S.
General correlations in the decay of heavy mesons. Izv.AN SSSR
Ser.fiz.19 no.6:664 N-D 155. (KGRA 9:4)
l.Moskovskiy gosudarstvennyy universitet imeni M.V.Lomonosova.
(Cosmic rays) (Nuclear physics)

SHA,PIRO, I. S.
"Photo Nu-,lear Reactions and the Scattering of Nelitrons by Hight Nuclei" a
paper presented at the International Conference on Nuclear Reactions, Amsterdam,
2-7 July 19156.
D551274

Category USSR/Nuclear Physics - Elementary Particles C-3
Abs Jour Ref Zhur - Fizika, No 1) 1957) No 438
Author Shapiro, I.S., and Estulin., I. V.
Imst -,LTo-s-c-ow--Sfa-~Ee-University, USSR
Title On the Electric Charge of a Neutron.
Orig Pub Zh. eksperim. i teor. fiziki, 1956, 30, No 3, 579-580
Abstract A narrow beam of thrrmal neutrons, filtered by graphite, with an average
kinetic energy of 0.026 ev, was collimated by two foils of cadmium with
slit apertures 2 mm wide, placed 50 cm. apart. Two aluminum plates were
placed in parallel with Uze planes of the slits. The plates were 50 cm
long, and the distance between them was 7.5 mm. The difference of potential
between the plates was 10 kv. If the neutron charge is qe, where e is the
electron charge, then the electric field of the capacitor should deflect the
beam by A x - qeE12/4w, where E is the blectric field intensity and W the
kinetic energy of the neutrons. The experimentally observed displacement of
the beam was less than 0.02 mm, corresponding to q less than 6 x 10-12.
Card 1/1

SUBJECT USSR PHYSICS CARD I / 2 PA -- 1373
AUTHOR SAPIRO, I.S.
'1ITLE The Peculiarities of the Levels of Nonspherical Even-Even Nuclei.
PERIODICAL Zurn.eksp.i teor.fis, 30, fase.5:, 975-977 (1956)
Issued: 8 / 1956 reviewed: 10 / 1956
Here the properties of the levels with 2 = 0 are investigated. sum of -the
projections Wi of the angular momenta of nucleons on the axis of the nucleus)-
Like in the case of the E-terms of a two-atom molecule a quantum numberl - + 'I
0~:ours in addition in the caseR - 0, which charaoterizes the behavior of ;he
wave function on the occasion of a reflection of the space with respect to a
plane passing through the symmetry axis of the nucleus. On the occasion of this
A
transformation the wave function TR P in converted into I 'F-S~P' Because
of the invariance of the HAMILTONIAN of the system with respect to the trans-
formation investigated, every term is twice degenerated with respect tos? . Here
P - + I denotea the parity of the state. in the case of 0 it is true that
1, and therefore it is possible that, instead of de-
470P 7t -
generation, twb levels with differdnt values of 11 exist. States withS~ = 0 can
b occur in nuclei with even A and obviously especially in even-evea nuclei. Among
i. them are e.g. the ground state (J=O, P= +1) and the first excited state (J=2,
P=+1 ). These two states of even-even nuclei have the same 'I . I'Vith 7L the f ollow-
ing selection rule for the radiation transitions is connected! The transitions
betyreen levels with the same 'q (or with a change of sign for IL ) can be only of

11 p D-- -a,,,r ;nd :bneonservation of Pntrit-,," (relri,%w lectullre)
21obcow state Univ.
.1 n an Lo- n gy
-.a~-ier su !dtted at the A-U Conf. -z. ~.uclear 'eactions it -led.;.un. d -.- - er
--,csco,.:, Ic-27 "cv 57.

*~'NZEL. Donald H., red.; KAZARITOVSKIY, N.V. (translator]; TIKH%IIROV, F.A.
[translator); ARNOLID, N.A. [translator]; PBTRUKHIN, V.I. [translator];
KATSONASHVILI, B.H. [translator]; AKSENOV, S.I. [translator];
BAKANOV, S.P. [translator]; HAPIRO.J.S.. red.; ADIROVICH, E.I.,
red.; MEDVIDEV. Yu.T.. red., RAKHiM'SON. I.G.. red.; TEUSNIff, H.L..
red.; BELLTA, M.A., tekhn.red.
[Fun(lamental formulas of physics. Translated from the English]
Osnovnye formuly fiziki. Moskva, Izd-vo inostr. lit-ry. 1957.
657 P - (MIRA 11:5)
(Mathematical physics)

o
~ L

0

ON THE UMRACMN ]BETWEEN
-jiMES016 ANb
CLEONIK reL

Go
-

-.Mw agw9ar,
&d3qbit6 mad towt
pol"Usam of
b tho esove ofp,! M"*=
an ou~,. *tb)

E3d

ESTiO
U N OF THEAPD-1AND E&Wj OF THE
~Om THE !
f
Y
ES Dollaskil, and A. P.
--J~M ON
Unly.). Soviet PhYs. JETP 5,
129-30(1957) Aug..
A comparison of the experimental data on the energy
'
&pactIruin and azj~lu distribution of their
Mesons formed
'
In positive and nagativa
i docay with theoretical curves
leads to the conclusion that the moat probable spln and
parity values for the: meson are 0~., (L.T.W.)

XUTHOR SHAPIRO, I PA - 2084
DOLINSKIj', 1".I.
MISHAKOVA
A.P.
TITLE ,
,
On the Spin and Parity :I ~he 3--bleson (K voprosu o spine i chetnosti
3--mezona).
PERIODICAL Zhurnal Eksperimentallnoi i Teoret. Fiziki, 1957, Vol 32, ~1r 1,
PP 173-175 (U.S.S.R.)
Received 3/1957 Reviewed 4A957
ABSTRACT On the strength of consideration which formerly have not been taken into
account, the present work shows that experimental data exclude the pos-
sibility investigated by MARSHAK. The authors hereby base on the following
considerations. 1) The isotopic spin I3R of the system of 3 pions occur-
ring on the occasion ofy-decay is equal tp 1. This assumption made also
by other authors results from the GELL-MANN scheme according to which the
7 -meson has the isotopic spin I-y = 1/2. The slow decay 7+.,- ff+ + n+ + V-
can be explained by the non-conservation of isotopic spin. 2)K-mesons which
decay according to the scheme III -+ v� + 2TrO are identified with r-mesons.
3) According to various experimental data Wi/wrl - 4 is true for the ratio
of probabilities of I- and TI-decay. Asnwaing validity of conditions 1)
and 2), it holds that Wj-1W 71 = (hF + 6)/(F + ~). Here'F denotes a quan-
tity which can be obtained by integr~-.-uin-c-, the squares of the moduli of the
matrix-elements, which are symmetric with respect to the momenta of all
pions, over the energies of the pions. (P denotes an analogous quantity
which can be obtained from the matrix-elements which are symmetric only
with respect to the momenta of the identical pions. It is found that(~- 0,
i,.e. pions are produced only in states that are symmetric with respect to
Card 1/2

PA - 2084
On the Spin and Parity of the ')J-Meson.
the momenta of all 3 particles, If this assumption is correct the spectrum
of positive pions in the case of .71-decay must be identical with that of
positive pions in the case of-r-decay. The lowest orbital momenta cor-
responding to these data are given in a scheme which contains also the
orbital momenta and matrix-elements used by DALITZ. A diagram shows the
curves for the energy spectrum of pions which have been computed from the
matrix elements of the synmetric states. The curves corresponding to the
spins and symmetries (parities) 1+, l-, and 2+ differ considerably from
the experimental spectrum. Also the curve for thu case 2- agrees less well
vidth the experimental. value than the curve corresponding to case 0-.
Some conclusions. i0 The cnn~bination 0- is the most probable for spin and
parity. B) CornbinatLons 1+,. 'i_., and 2' are practically excluded. Thus the
most probable val-leS L;.6p_cii.11y L,~osc_ ti~at lead to an occurrence of
the so-called ;' 3-(-) 11 -problem. (I illustration)
ASSOCIATION Moscow State University
PRESENTED BY
SUBMITTED
AVAILABLE Library of Congress
Card 2/2

AUTHOR _S~UPIRO I. S. PA 3o63
TITLE On the Non-Conservation of the Parity at the P-Decay.
(0 nesokhranenii chetnosti pri P-ras;ade - Russian)
PERIODICAL Uspekhi Fiziahe8kikh Nauky 1957, Vol 51, Nr 3, PP -ZJ3 -Z-,o
(USSR)
Received: 5/1957 Reviewed: 7/1759
ABSTRACT After C.S. Wu et alii, and L.M. Lederman et klii, respeotively
(Phys Rev. 1957,in print) had sueseeded in determining experiment-
ally the anisotropy of the angular distribution of the elestrons
at the P-desay of polarized nuelei and at the de*ay of jW-mesonsq
respectively, this hypothesis must be considered to be verified.
The following possible explanatiohs are listed:
(a) Inner asymmetry of the partiele, in analogy to the molesules
of tartarie asid. Partioular reference is made to the hypothesis
by L.D. Landau (Zh. E.T.F., Vol 32, Nr 2), assording to whish a
transition to the #mLirror partiele' simultaneously means a
transition to the antipartiele. Therefrom and from the
longitudinal neutrino hypothesid' it is possible to derive
sonalusions whish are not in sontradistion with the experiments.
CA-RD 1/2

AUTHORS: Shapiro, I. S., Dolinskiy, E. I., Blokhintst3v, L.D., 20-6-14/42
TITLE: Problem of Int~-raction of lulcn (K vo-prosu
o vzaimoueystviid4.-mezonov s nak-iona_nii)_
PLRIODICAL: Do'--lady AN SSSR, 1957, Vol. 116, lir 6, pli. 9,1~6 - 946 (USSR)
ABSTRACT: The present report investigates the anualar distribution of neut-
riad which were obtained at the capture of a ne3ative muon by a
proton in d"-mesohydrogen. The negative muon is ajaumed to be po-
larized. In V i,.s case nE; an-alar diaLri,)ution of the neutrons in
t
a general case will be 3enerally anisotropic because of the -Ylon-
.darity with weal: interactions, in which case
conservation of the
both the sign and the size of anisotropy depend on the form of
interaction.The energy of interaction of a nuon with a nucleon
taking account of the nonconservation of parity can be written
down conjugated complex in the form H--7-(TnOk_Tp)(T4[9k-g' e5jkfel) +
k k
In this case Ok means the operators k-nown from the theory of the
B-decay which are composed of the Dirac matrices. It further holds
k - 5;tplv,a,t,in which case s,p,v,a,t signifies the scalar,pseudo-
scala3z,vectorial,pseudovectorial,and tensorial variant of inter-
action.With 9k - -gk the variant proposed. by L.D.Landau. (refer-
ence 1) of the theory with a longitudinal polarized neutrino is
obtained.The formula W (6)= 1 +acos6, holds for the an-ular distribu-
Card 1/2 tion of the neutrons,in which case 9 denotes the an.-le between the

Problem WInteraction of Muon With Rucleons.
2o-6-14/42
direction of emission of the neutron_ and the ne-gative direction
of polarization of the nel-lative muon. The terms valid in the ca-
se of the presence of all variants of interaction is given for a
The values of a for the differnt variants of interaction (on the
assumption of longitudinal neutri-no)are summarized in a table.Such
formulae can also be obtained for the capture of negative muons
by protons which are bound to nuclei.In this case a depends on
the matrix elerients of the nuclei which renders the interpretat-
ion of the experimental data difficult.Besides the anisotropy of
angular distribution of the neatrons, also the fact can be utili-
zed for the determination of the form of interaction that the
neutrons formed during the process & +p---;Pn+O are generally pola-
rized. This polarization takes place both transversally and long-
itudinally. A table contains the amounts of longitudinal polari-
zation of the P-neutrons obtained at the capture of unpolarized
negative nuons by free protons in the case of a longitudinal
neatrino.These data hold also approximately for the capture of
muons by nuclei.There are 1 figure,1 table and 4 references,2 of
wiiich are Slavic. (vennvv universitet im.M-V-Lomonosova)
ASSOCIATION:, Moscov State University im. M. V. Tanonosov (&skovskiy gosudarst-
PRESENTED: May 27, 1957, b.: D. v. oKobelltsyn,Acaderician
SUBMITTED~ May 18,1957
AVAILABLE: Library of Con.aress
Card 2/2

LMANOV) A. v.., ORLOV., Y. V. J. TMONOV, A. N., TLIROV7WV, V. V. and SHAPIRO, 1. S.
"La Models Optique pour 11interaction avec lea noyaux des neutrona dlenergie moyanne."
report presented at the Intl. Congress for Nuclear Interactions (Low Energy) and Nuclear
r Structure (Intl. Union Pure and Applied Physics.) Paris, 7-12 July 1958.

5M PWE I BOOK EXPLOITATION - "--SGV/1223
Shapiro, losif Sofamonovich, Doctor of Pbysical and Mathematical Sciences
Elementaimyye chastitsy (Elementary Particles) Moscow, Izd-vo "Me-1ye,"
1958. 31 P. (Series: Voesoyuznoye'obshchestvo p0 rasprostranenlyu,
politicheskikh i nauchnykh znaniy. Seriya VIII, 19589 vYP- 11, no- 17)
35,000 cipies printed.
Sponsoring Agency: Vsesoyuznoye obshchestvo po rasprostraneniyu politicheskikh i
nauch nykh znaniy.
Ed.: Faynobym, 1.B.; Tech. Ed.: Berlov, A.P.
PUF(POSE: The book is intended for the general reader.
COVERAGE: The book is concerned with the present status of the ybysics of
elementary particles. A description of the propertiekof elementary partidlea
is given and their interaction, formation and decay are diseussede No person-
alitles are mentioned. No references are given.
Card 1/3

"ILIi

DENISOV. F.P.,red.; LAZAREOVA, L.Ye.,red.; LEYKIN, Ye.M.,red.; ROZHANSKIY,
I.D.,red.; FRANK, I.M.,rud.; SHAPIRO, I.S.,red.; SHAPIRO, F.L.,red.;
POLF10VA, T.P.,tekhn. rad.
LLow and intermediate energy nuclear reactions-, transactions of
the conference] IAdernye reaktaii pri malykh i srednikh energiiakh;
trudy konferentaii. Mosim, Izd-vo Akad. nauk SSSR, 1958. 614 p.
(MIRA 11:12)
1. Ysesoyuzziaya koriferantsiya po yadernym reaktsiyam pri malykh
i Brednikh energiyakh. Moscow, 1957.
Ouclear reactions)

4 UTH' OR Shapiro, I. S. SOV/53-65-4-13/13
TITLE: Bibliography (Bibliografiya)
PERIODICAL: Uspekhi fizicheskikh nauk, 1958, Vol 65, Nr 4,
pp 739 - 739 (USSR)
ABSTRACT: The author gives a detailed discussion of a handbook
entitled: 11 New Symmetrical Properties of Elementary Particles".
It is a selection of papers edited by I.M.Khalatnikov. The
work was published 1957, it has 97 pages, and the price
is 5,10 Roubles.
Card 1/1

SOV/25-59-~
o,, P~11,yi~jcaj and em-tic 1,1
J` OR: Sha
IH piro, 1.2., j)octor
ociences
TITLE: "Strange" Particles
1:~E-:UIODICAL: 11auka i zhizn", , 1959, Nr 7, rp 9-13
The article b~;.sed on forei,-,n rosearch ~iv,~s a suiv--~Y
of the la-test findings in elefuenuary particles research,
up uo tUhe year l-,58. It is divided inzo -t-ie folic.--vin6
J
7 secu"ions; 1.) Fref-,,ce; 2) "Distinctive of Z11-e-
mentary Particles; 5) Classification of tno `-'a-otlclos;
la-ticles and .1-uti-P-z-rticles- ,Ily
_,ra-
Hyperons -are Called "Stran Di3inte,-
tion of "6tran.u-,---" Particles, 7) ;:Jouble-Faced" Fur-
ticle. There are 2 dia.:.e.-rams ar-id 2 set.3 Df dia,-:-r!~as.

111:~; Shapiro, I. S., Blokhintsev,
';'ITL-E', Circular Polarization of the
After a (c(7-Capture
L,;,;11()D1CAL-.
Ab"'IMACT.
d 1/4
L. D. sov/56-37-3-26/62
r-Quanta Emitted by a Nucleus
Zhurnal eksperimentallnoy i teoreticheskoy fizikip 1959,
Vol 37, Nr 3(9), PP 760-764 (USSR)
In computing the circular polarization mentioned in the title
the hyperfine splitting up of the level of the mesic atom was
taken into account. The authors made their computations for the
case that the nucleus passes to a discontinuously varying level
in the e7-captuxe (i.e. no neutron departs). The process to be
investigated is the following: Nucleus A Z with spin j, captures
a polarized negative ion from the K-shell and passes to the
excited level A Z-1 with spin j 21 which then passes from the
multiplicity J to the ground state with spin j 3under emission
of a r-quantum. The authors wrote down the Hamiltonian of the
four-?ermion interaction as'a superposition of the vectorial(V),
axially vectorial (a), and pseudoscalar (p) variant with the
coupling constants g , g and g . The degree C of circular
V a P

C~ rc~L_l ar Polar_'zation of the r-quanta Rmitted by SOV/56-37-3-26/62
a Na~leus After a ~~'-Capture
polar-Lzation is defined as follows: cr =(W+ - w_)/(W+ - W-)
W and V[_ denote the probabilities of the emission of r-quanta
with their spin in parallel (right-hand polarization) and anti-
parallel position respectively, to the momentum (left-hand
polarization). For a longitudinal neutrino the computation
furnishes the result: C = P., acos 0 , ce, = B/A. P
r ,, denotes
the degree of polarization of the negative muon at the instant
of its incidence on the K-orbit of the mesic atom, e - the angle
between the directio" of the polarization vector of the
negative muon and of the direction of departure of the t-quantum.
The above-mentioned formulas hold f.or the case that the neutrino
departs with a certain angular momentum A = A min . This is the
-Least possible angular momentum admitted by selection rules. The
oorrection shown by Gel!-Mann (Ref 4) concerning the allowed
transitions due to the "weak mechanism" has already been taken
into consideration in the above expressions. In order to examine
this, the authors investigate the transition
Card 2/4 1 (no). A formula. is written down for the
Ai J2 - i1 = �

Polarization of the r-Quanta Emitted by SOV/56-37-3-26/62
Nucleus After a AL--Capture
matrix element hf, of the elz transition. The structure of this
matrix element M V is similar to that of the matrix element of
the operator for the energy of interaction of the magnetic
moment with the magnetic field, Quantity eu. (the total magnetic
moment of the transition, computed in nuclear magneton units)
takes into account the contribution of virtual pions according
to Gell-Mann.(Ref 4). For the transitions of the type
A j = ;t I (no), however, neither corrections are made for a
I'weak mechanism" nor are other relativistic corrections of the
same order of magnitude applied to the amount of polarization
of the 1--rays although they contribute to the total probability
of the process. The problem of such corrections in the
(a----,apture was investigated more exactly by B. L. Ioffe (Ref 5).
In computing the expression for C r the hyperfine splitting-up
of the mesic-atom level was taken into account, for it plays an
important part. In the transitions satisfying Fermi's selection
rules the circular polarization of r-quanta is entirely due to
hyperfine interaction. As an example of an allowed transition
.3/4

1;j z - u"-ctz~ Polarizatit)n of the t-Quanta Emitted by SOV/56-37-3-26/62
e-as Af ter a ~~-Capture
,,,iith subsequent dipole radiation (A = o, J = 1) at
1/2 is investigated for the Gamov-Teller v,-riant.
Ji j2 = j3 ~ '
In most cases, the 6Z7-capture leads to the departure of a
neutron from the nucleus. There are 7 references, 3 of which
are Soviet.
SUBMITTED- April 3. 1959
Card 4/4

SHAPIRO, I.S.
"Capture and Structure of Light Nuclei"
report submitted for the 2nd USSR Conference on Nuclear Reaction at Low and
Intermediate Energies, Moscow, 21-28 July 1960.

83613
S/056/60/038/005/046/050
?,00 B006/BO63
AIMORt Shapiro, 1, S.
RadiatAonless Decay of a a-Me /?nto an Electron
T son
Pe,RTODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 196o,
Vol~ 38, No, 5, PP~ 1646 - 1647
TEXT: The radiationless decay of a muon-into an electron in the Coulomb A/
field according to (1)1~b + AZ -+ z+ e was investigated by Weinberg
and Feinberg (Ref. 1) by the example of four-fermion interaction of the
.Ype (e,~ (tf) (f - charged particle). Steinberger and Wolfe determined
the relative probability of this auon decay (with respect to the ordinary
64 4_
rtz-orz capture by protons of the Cu nucleus) to be!~-~ 5-10- Th,v
attempted to determine this decay by recording 100-Mev elactront-A. Th-',
present "Letter to the Editor" describes another possibility of
determining reaction (1). The-author studies a light~L-mesic atom having
12 16 20 of
an even-6ven' nucleus (C 0 or Ite For excitation energies
Card 1/2

SHAPIRO, I.S.; GAPONOV, Yu.V.
Continuous representation of total Green's functions. Vest.
Mosk. un. Ser. 3 Fiz., astron 16 no.2:73-81 Mr-Ap 161.
(MMA 14-.6)
1. Nauchno~issledavatel'skiy institut yadernoy fizJ-ki,
Kafedra yadernW spektroskopii.
(Boundary value problems)
(Functions, Continuods)

1. 7 i2
SA056/61/041/005/027/038
B102/B138
AUTHOR: Shapiro, I. S.
TITLE: Dispersion theory of direct nuclear reactions
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, v. 41,
no. 501), 1961, 1616-1627
TEXT: The author uses the Feynman graph technique together with the
dispersion relations to study direct nuclear interactions of the type
A +x B + y . First he formulates the kinematic relations and
B + y + z
unitarity and analyticity conditions for the reaction A +x .. 0, B + y. This
can be expressed by two of the following independent variables. the
kinetic energy E of the colliding particles, the square momentum
2 2 2
transferred q (p y -Px) , or the square momentum sum p = (PX +pY )2.
The unitarity condition SS =I is defined for S = 1 + i(2.)4T, T + iJ4
with (2'E)4 ZT T and
if 2 n in nf
Card 1/6

2671-2
S/056/61/041/005/027/038
Dispersion theory of direct nuclear... B102/B138
Tk-j (q2, E) A[~-j (q2, E) 6xk.).[ (10)
,11,1 (q2, E) A fj (q2, E) fit)
The arguments of the 6-function are the momenta and energies of the
states k and 1, the subscript X indicates the totality of discrete
2
quantum numbers. The amplitudes Mk1 (q, E) are analytic functions.
Assuming that the main contribution to the amplitude of a direct nuclear
process comes from Peynman graphs with singularities which are clospst to
the physical region of the variables, the contributions from the poli-I
2
diagrams (Pig. 1) are investigated. At pb. 2mbEb the amplitude Mif
(transitions f -n,-.i--,,n) has a pole, near which
Mif = 2nib 61 (14).
P2 - 2flIbEb - '9
The subscript b indicates the quantities of the compound particle b.A
Card 2/6

S~056~61/041/005/027/038
Dispersion theory of direct nuclear... B 02/ 138
singular integral equation to allow for the interactions in the initial
and final states is obtained from the energy dispersion relations for the
graphs of Fig. 2.:
ivi), (E) J- dE'. (31)
'If X
E'
E. L/
M0 (E) denotes the sum of all pole terms and E = 0 Q0 0
liberated energy. From this equation in zeroth iteration Mxy MXY
(Butler theory) is found, and in first iteration
1 C-a~ p., (E') ii f(E') f.,,, (E')
_0 E'- E - iij
(34)
1) (E') fM.,,, (E').
ill Y
E,
(method of distorted waves). The criteria of convergence of this
iteration procedure are discussed. An investigation of triangular graph
singularities shows that besides the pole graphs corresponding to the
Butler mech~inism and to exchange stripping and heavy pick-up reactions,
Card 3/6

j
S/056/61/041/005/027/038
Dispersion theory of direct nuclear... B102/B138
more complex graphs can also make a significant contribution to the direct
reaction me,~hanism. This is illustrated for the reactions Be'(a,t)B'O,
Be9 (d,n)B 10 and C12 (d,p)C' 3. Finally the mechanism of some reactions of
the type A+x B+y+z is considered analogously. Peculiarities of reactions
in which "clusters" of particles are nocked out of the nucleus are also
discussed. The author thanks L. D. Landau and K. A. Ter-Mariirosyan for
comments. L. B. Okun', A. P. Rudik (Nucl. Phys. 15, 261, 1960) and
N. A. Vlasov et al. (ZhETF, 39, 1468, 1960) are mentioned. There are
6 figures, I table, and 8 rJ_e~ences: 3 Soviet and 5 non-Soviet. The
four most recent references to English-language publications read as
follows: R. D. Amado. Phys. Rev. Lett., 2, 399, 1959; L. D. Landau. Nucl.
Phys. 13, 161, 1959; S. Ozaki et al. Phys. Rev. Lett. 4, 533, .196o;
G. F. Chew, F. E. Low. Phys. Rev. 113, 1640, 1959.
ASSOCIATION: Institut teoreticheskoy i eksperimentallnoy fiziki Akademii
nauk SSSR (Institute of Theoretical and Experimental
Physics of the Academy of Sciences, USSR)
SUBMITTED: June 3, 1961
Card 4/6

27484
S/053/61/075/001/0u)2//003
0 3 ~/ 13 JY, /131) B125/B108
AUTHOR: Shapiro, 1. S.
TITLE: The ortical model of nucleus in the light of modern data
PERIODICAL: Uspekhi fizicheskikh na uk, v. 75, no. 1, 1961, 61 - 100
TEXT: Accordingbo'experimental and theoretical results of 1956 - 1960,
nuclei are nqarly as transparent for complex particles (deuterons,
aL-Darticies).as for nucleons.* The optical model for the sca-ttering of
nucleons: Experiments do not confirm the theoretically derived monotonic
increase of the scattering cross sections with increasing A and energy E.
The Pauli principle is the principal cause of the unexpectedly sharp
diminution of the scattering cross sections of coupled nucleons..
The theoretical results hold also for nuclei of finite dimensions. The
model with rectangular.potentials such as U(?) = -V(?)(l+i�) (17) with
V(r) o, r ( R --vlvo, (U(P-) - -Vcv-) - iw(l')) give's too high ratios
~O , r>R
Card 1/4

27484.
S/053/61/075/001/'002/003
The ontical model of nucleus ... B125/BIOS
cr, = crl/cp The continuous decrease of U(-i~) toward zero must cause an
0 s Tr Jf2
increase of cy crt is the total cross section, cr. - 2-.r sin&&
r t s 0
The crtical model with continuously decreasing nuclear potential was
inveE!-;igated by P. E. Nemirovskiy (D,A1,T SSSR 1011 257 (1955)) for neutrons.
An ar,--quaie choice of the model parameters gives a good agreement of
expe -imental and theoretical values of crt and cr for medium and heavy
0
nuc.'ai. The theoretical value of a, for light nuclei is too high. The
0
opt cal model describesalso the distribution of scattered neutrons. The
d.e-,,~~ndence of the uotential on the nucleon spin-orientation leavescy s and
ir practically unchanged, but it may essentially diminish the intensity of
I -
~'e scattered nucleons for angles -7r. Incident nucleons may be polari *zed
ii the direction O'by spin-orientation-dependent scattering. The polari-
zelion P4. = (i - J + J is zero for 13 = 0, ir. J and J are the
V + -)/(J+ +
numt,,:-j of nucleons scattered through the angle -&, whose spin projections
s upon the direction iY have the values 1, respectively. Tie above-
z :5
Card 2/4

27484
S/053/61/075/001/002/003
The optical model of nucleus ... B125/B108
mentioned facts requi rP,_,a spin-orientation-deoendent potent:.al matrix
U(r-") = U(r).1 + Vs(r).i~, s - e12, where U(r) is the usual central
potential. The optical model leads to correct absolute values of P(bq)
and to the dependence of polarization on the scattering angle-&. Scattering
ofr~_-particles: The optical model with diffuse periphery is in good
agreement with the experimental data concerning the scattering of
c-particles. It describes almost exactly the details of angular
distribution. The best agreement with experiments and the best constancy
of the Darameters was attained with the model with surface absorption.
Scattering of deuterons: Nuclei are transparent for deuterons with an
energy of 10 - 15 Mev. Table 11 gives th~ parameters of the optical
potential for deuterons. The scattering of heavy ions may also be
described in a satisfactory mariner-by the optical model. A good agreement
between theory and experiment is also given by an optical model with
volume absorption and with the following values of the optical potential:
V = - 13 cm, a = 0.575-10- 13 cm. The
0 48 Mev, "'to 5-75 Mev; r. . 1.275*10
application of the optical model to direct processes also appears
Card 3/4

2704
S/053/61/075/001/002/003
The optical model of nucleus ... B125/B108
interesting and promising. There are 29 figures, 11 tables, and 2A, -refe-r-
ences: 6 Soviet and 17 non-Soviet. The three most' recent references to
English-language publications read as follows: L. Rosen, Proc. of the
Intern. Conference on Nual. Structure, Kingston, Canada, 1960, p. 1851
H. L. Reynolds, E. Goldberg, D. D. Kerlee, Phys. Rev. 119, 2009 (1960);
R. H. Bassel, R. M. Drisko, Proc. of the Intern. Conference.on Nucl.
Structure, Kingston, Canada, 1960, p. 212.
Table 11. Parameters of the
o
i
pt-cal.potential for deuterons.
Legend- (1) deuteron energy (Mev),
(2) element, (3) Mev, (4) Ferg'.
Card 4/4
Da e11T
eX 126
VO (3
(31,
30) a (Oep-u)
Ni 59 19 1,43 0.63
1-14,5 511 60 10,5 1 .60 0,62
Au 50 9 1150 0.66
Al 55 25 t.50 0,60
Ti 59 21 1.50 0,60
11h 52 t2 1,62 0,60
15 SU 55 11 1,60 0,58
Pd 53 11 1,62 0.58
Ta 48,5 9 1.5.5 0.53
Au 50 9 1 %5 0.66
Pb 48.5 9 1,52 1
i 0.63

I'. it. rjid 1. S.
~, I
, . !:, 1 " r. I -.: -: - I- ~ 7 -1 n
Pn---'c:-.,cd at the ir-;LL. (-n.'crencc C-r- HIF~;
!-I! ildy j~-,Il
~.: ~ -. ': ,

SHAPIRO) I. S.
'~Expansion of Scattering Amplitude in Relativistic Spherical F~Mctions"
report presented at the Intl. Conference on High Erergy Physics, Geneva,
4-1-1 july 1962
Inst. of Theoretical and Experimental Physics, Moscow, USSR

SAPIRO, I.S. (Shapiro, I.S.]
Nuclear optical model in the light of contemporary data. Analele
mat 16 no.3.*94-IL39 JI-S 162,

5/050'/62/043/003/050/0")3
3108/B102
AUTHOR: _iLa i ~ro I ~__
TITLE; Vertex parts of the amplitudes of'direct nuclear processes
PERIODI.CAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, V. 43,
no. 3(g), 1962, lo6a - 1082
TEXT; The vertex parts previously introduced (ZhETF, 41, 1616, 1961;
T
W
~jcl. Phys., 28, 244, 1961) are studied by using the optical model. The
analytical properties of the vertex part as functions of the momentum
transferred are investigated. The diffuseness of the edge of-the
potential well in the.optical nuclear model leads to singularities in the
vertex part. An essential singularity in the transferred momentum at
infinity corresponds to the nuclear radius. The vertex parts are expressed
in terms of the parameters of the optical model. The resulting formulas
can be used for practical cases since the optical model is a good
description of interaction between nuclei and nucleons or even more
complex particles. There is I figure.
Card 1/2
I

S/056/62/043/Q-03/05 0/06 z
Vertex parts of the ... Bio8/3102
AS'.-~ 00 1 A T ION: Inst!itut teoreticheskoy i eksperimentallnoy fiziki Akademii
naukLSSSR (Institute of Theoretical-and Experimental
Phys Cs of the Academy of Sciences-USSR)
SUB~,HTTLD: Aprl 20, 1962
Card 2/2

S/056/62/043/005/026/058
B102/B104
AWHORs Shapiro, I. S.
TITLEi Expansion of scattering amplitude in relativistic spherical
functions
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki,, v. 43,
no. 501), 1962, 1727 - 1730
TEXT: The scattering of two spin-zero particles of equal mass,/- is con-
sidered. From the dispersion relation with respect to the transfered
U(t's) 12
momentum it follows that the invariant integra
l Mt N -
, !(t-a )n,
n ',0) will converge. Hith Z
;>O
(a p0P/ic2it can be br ought to the form
.
,
c0
N 4nx2 If (Z' S) 12 VZ2 _I dZ, (I a)
(Z, s) U (t, s)l(t - a)". (3)
Card 1/5

S/056 62/043/005/026/058
Expansion of scattering... B102 B104
where p 0and p are the four-momenta of the incident and of the scattered
particle, E. is the energy of the latter. U(t,s) is the scattering
3p/Y'2F
amplitude in Mandelstam v3riables. Since d _ is an element of the unit
sphere, (1) can bo considered as an integral over the surface of the four-
dimensional sphere of a function of p. Thus the problem can be treated
analogously to that of finding the expansion of the scattering amplitude in
threedimensional spherical functions. In the present problem the operator
1
F M bi (angular four-momentum) will be the expansion quantity;
,,, V ~Lv
ii,v-1,2,3,4, Y, -i(p a/apv - Pa/ap,,). This expansion was already ob-
/4 /L I
tained in 1955 (1. S. Shapiro,'DAN SSSR, 1o6, 647, 1956) by using the
theory of Lorentz group representations. The pair ji, j2 of the usual
irreducible Lorentz group representation is replaced by m,q where
m 202-i1) and Q--2i(.j l+j2.tl ). These numbers determine the eigenvalues
of F 3nd of the invariant pseudoscalar commutation operator
(M 2_Q2)/4], G - -mQ, where m is an integral
Card 2/5

3/056/62/043/005/026/058
Expansion of scattering ... B102/B104
and Q an arbitrary real number. For spin-zero particles G 0 and m 0,
so that
j .1 . - pn)-t+ip' 12 'Idp,
(P, S) C (P, S, n) p (8a)
f
C (p, S; n) f (P, S) n) -1-4012 d3p (86)
C it! p2dp d,,, I f 12 (9)
is obtained. After integration with respect to the solid-angle element
dt,)n , and considering the fact that C(q,s;n)) does not depend on n, the
functions and c(QI,s) are obtained * QI-912 are considered as
relativistic invariants; so likewise are the particle amplitudes c(Q,,s).
Eliminating s, these functions can be represented as
Card 5/5

Expansion of scattering...
p'sin(pp: dp'dp'~,
C W, P,;) sinx
2
C(P" PI) (p) sin -tp'sin T p', dXdT
Ch (p = Y s/20 - 1,
(Z' Y)
which solve the problem in this form. From
S/056/62/043/005/026/058
B102/B104
(I 3a)
(136)
(14)
V, (Z.. v,.n)-'-' dw.=
sin pX, (16)
Card 4/5 z = Z,Z, -4- 1, V21 = V" (16a)

Expansion of scattering ...
the unitarity condition
S/05 62/043/005/026/058
B102YB104
I in C (p, s) = 32X4 Ins (s - W)J-Iil C (p, s) t1P X
P 2
c0
X C' (p, s) IL sin Pq d1i,
2
0
(17)
can be obtained for the two-particle intermediate state.
1W 2 C(Q,s) are particle amplitudes of the U(s,t) matrix
4Y, Uab
which is related with Tab by Tab - (2n)' b(pa-Pb) From (17)
41,41;: - -
2~3 ~'4
IMC(Q,s)/ReC(Q,s) - Q(s) follows.
ASSOCIATION: Institut teoreticheskoy i eksperi~entallnoy fiziki Akademii
nauk, 5_245R (Institute of Theoretical and Experimental Physics
of the Academy of Sciences USSR)
SUBYITTEDs May 8, 1962
Card 5/5

S/056/62/043/005/035/058
B102/B104
AUTHORS: 1,obov, G. A., Shapiro, I. S.
TITLE: Radiative capture of a x -meson by a proton
PERIODICAL: Zhurnal eksperimentallnoy i teoret'icheskoy fiziki, v. 43,
no. 5(11), 1962, 1821 - 1825
TEXT; The contributions from induced pseudoscalar interaction to the
radiative muon capturew +p--)Pn+%)+ are investigated. In contradistinction
to previous papers Uhys. Rev. 11~, 354, 19j8; 115, 694, 1959; Rev. Mod.
Phys. 51, 797, 1959; 51, 802, 10/59)q all graphs (Figs. 1, 2) are taken into
account. It can be shown that the contribution from the graphs of Fig. 2
is comparable with that from Fig. 1. The-prob3bility of radiative muon
capture depends stron6ly Qn sign and magnitude of the pseuduscalar coupling
constant g.. Photonspectra due to the above graphs and photon circular
polarization are calculated (Figs. 3, 4). The amount of circular polariza-
tion ([.) is strongly affected by the presence of induced pseudoscalar
interaction; change in sign of g P changes_~ by a factor of 5. Taking
account of the graphs 6' and 8 of Fig. 2 raises the probability of radiRtive
Card 1/3

S/056/62/043/005/035/058
Radiative capture of ... B102/3104
-capture by almost 10G-p; change in sign of g,:, reduces this probability
from',',=10.2-10-2sec-1 for g,, +6g, to 'i=4.2'1O_2 sec- 1 for g -6g
A'
The radiativep- capture Gue to induced pseudoscalar interaction and the
V
processes n+l--),TE-+p anG n+--- /,+ + are interrelated since the matrix
element of the radiative capture in polE. approximation can be expressed
in terms of the form facturs of the latter processes. There are 5 figures.
ASSOCIATION: Institut teoreticheskoy i eksperimentallnoy fiziki Akademi4i
nauk ~SSt (Institute of Theoretical and zxperimental Physics
of the Academy of -'Ciences USSR)
SUBMITTED; June 1, 1962
Pig. 3. -Spectra of the photons emitted in p, capture. L for graphs of
Fig. 1 only,, for all graphs with g -+8g Ll,- for all graphs with
9P .-8g A' P .A'
Fig. 4. ~(x) for + (A) an-- - (B) sign of g.; x is the photon energy in
terms of its maximum unergy.
Card 2115

Radiative capture of ...
Fig. 1
/7 V
V
X-
Fig. 2
B/056/62/043/005/035/058
B102/B104
17 V 11
lz Ir 17
17 ~'
I
1,.
,U
Fig. 4
Card 3/3
Vs
Z-~
X
0.2 04 0 08 40
Fig. 3

S/056/63/044/001/047/067-
102/B186-
W
AUTHORS: Kolybasov, V. M.
TITLE: The mechanism of it capturp by light nuclei
PERIODICAL: Zhurnal e.keperimentallnoy i teoreticheekoy fiziki-q- V-- 449
no. T, 1963, 270-271
TEXT: N. V. Rabin et al. (Phys. Rev. Lett.., in press) have shown that when's
12 16
n- mesons are stopped and captured by light emulsion nuclei (C or 0 a
number of p, d, and t are emitted with E >25 Mev. since this energy 16
much greaterthan the nU'clear temperature, such emissions must-be due.'to
direct processes, e.g. interaction of n- with nucleon groups such as
He2, He3 or a. On the bas .is-of dispersion thmiory, using the pole tiaph'.
formulas obtained by Shapiro (ZhETF, 41, 1W, 1961), the-relativt enissidn
probabilities for p, d,-afid t on n- capture are calculated,for C19i.. rt is*
assumed that the above-mentioned nucleon groups are a-p'articles-and that
the reaction amplitude ie-abnetant. Besides the relative yields Ahe..'.
energy spectrum of the partiolea emitted on n capture -is calculated. The
Card 1/2

949 a M -
4
S/056J63/044/001/47/06T
The mechanism of n capture B102/BJ~86:".
results are in relatively good agreem6nt with experimeiitai (tat 1 0.6--
n- capture by-nuclear a-particles can be considered the domi=
mechanism. There are 2.figures'.
SUBMITTED: July 26,. 1962
Card 2/2
OREM

L 5043-66 EV1T(d)/E'WT(m)/T/EWA(m)-2 IJP(c)
ACCESSION NR: AT5022314 UR/3138/64/000/256/0001/0080
if 1(;
AUTHOR: Shapiro, I. S.; Mandelltsveyg, V. Be (1,
TITLE: Lie groups nnd t4,~ symmetry of e~ -[q, Y~
.SOURCE: UJS~SR. ~Gosu~darst~ve~ kommitat IspolIzovaniy atomnoy lyl/
-P -0 - q ton-
:ener ii. Institut teoroticbeskoy I eksperimentallnoy fiziki.Dokj~&-AjPz5---
---ntarnykii ---bjas-irti-9'l-8O
!no. Plif), 1964. Gruppy sfim7etRY6 eleme c
iTOPIC TAGS: particle interaction, strong nuclear interaction.
'ABSTRACT: After a brief review of various pardmeters characterizing
~the strong interaction of elementary particles, the authors present
an extensive mathematical analysis and formulate the possible
asymmetries on the basis of simple Lie groups. The first part of the
:article by I. S. Shapiro deals with the structural analysis of Lie
!groups while the second part by V. B. Mandelltsveyg Is devoted to the
:character of irreducible representations of a selected SU3-group,
;In the first three chapters of Part I the basic designations and
equations for a continuous matrix group are presented, the similari-
;tiest isomorphisms and homomorphisms are examined and the normal
~'Oard 1/4

L
5043-66
ACCESSION MR: AT5022314
proper.
Chap,.,*~_.,~
divisor or the invariant subgroup is defined. The elementary
ties of Lie algebras are briefly summarized and three Lie theorems
are derived in Chap. 4 and 5. In Chap. 6 and 7 the normal divisor
and the structure constants for subgroups are discussed. Then an
invarient semi-simple criterion is derived including, the definition
of the necessnry and sufficient criterion conditions needed for a
group semi-simplicity. The problem of commutation correlations is
solved and a characteristic polynomial for the group with respect tc)
Xo-matrice,was presented in Chap. 8, The equation roots for a
characteristic polynomial of semi-simple groups are analyzed in
9 while Chap. 10 is devoted to the derivation of equations for the
semi-simple groups of the second class. It Is stated that the
simplest case of semi-simple group is the simple group.. Namely~'
these simple groups are mainly used now for theoretical discussions'-
of tile atrong interaction symmetriesi The classification of simple
groups is explained in Chap4 II and the results are illtistrat.ed.: bi
Card 2

L. 5043-66
i
,:ACCESSION NR: AT5022314
two tables& Chap. 12 (the last of Part 1) den1s with composing tits
root diagrams for tbe simple groups of the second class such as the
SU3, C2, and G2 groups. The first cbapter of Part II determines the
position of the SU3 group among the simple groups of the second clasi
From the theoretical point of view this proup seems to be the most
attractive for a further discussion. In addition to strong inter-
acting particles, this group also covers the weak and electromag-,
netic interaction symmetries. It survived experimental tests
although it is yet too early to make definate conclusions in favor
of the SU3-group. In Chap. 2 the selection of tensors is discussed
and the solutions of two theorems for various tensors are presented-
Two versions are considered of which the first version considers only
contravariant tensors while the second one deals with the tensors of
a symaetrical type. These two versions are separately formulated in
Chap# 3 and 4 including the Irreducible representations of the SU3-
grbup, the isotopic concept of supermultiplets and the solution of
three illustrative examples. The fifth chapter of Part II is devoted

L t504-LA-6
ACCESSION NR: AT5022314
to the deduction of the "mass formula" based on the article by
S. Okubo (Prog. Theor. Phys6 280 4._(,j.962)) and assisted by-Y# _Bo-,-:
1~-~aer~q~etskiyt I. t_~Yu-'~~;Kobzarevt LA,,B;7,-'UkunI and VVW~5ftaakov.A
gratitu~e'is expre-s'-se-d--b-'y--'t-he author-tior their participation. Orig,
art. has: 2 tables and 5 diagrams.
A5~3UWATIOM none
SUBMITTED: May64 ENCL: 00 SUB.CODIC., Mi. MA
no REP SOV: 004 OTHER: oil
Card 4/4

SIIAPIRO~, 1. S. ; TINMIIEVY S. F. j Moscow
"Direct reactions witn two-nucleon transfer."
report submitted for Intl Conf on Low & Medium Energies Nuclear Physics,
Paris, 2-8 jul 64.

LIU
~ pr ~~ f
Ya, ~ -- ','," I Va.. Ck
prcP V
1E."C. -ji akadernjj