SCIENTIFIC ABSTRACT LIVSHITS, M. S. - LIVSHITS, N. S.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000930310009-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 20, 2000
• Sequence Number: 9
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

USSR/Theoretica:l Physics B-4
'Abs Jour Referat Zhur Fizika, No 5, 1957, No 10860
Author Livehits ) M.S.
Inst Odessa Hydrometeorological Thstitute
Title Application of Non-Self-Adjoint Operators to Scattering
Theory.
Orig Pub : Zh. eksperim. teor. fiziki, 1956, 31, No 1, 121-131
Abstract : The elastic scatterinG of a particle passing through a
compound nucleus is considered. The spins of the parti-
cles are not taken into account. The author constructs
a scattering matrix for the particle and finds its con-
nection with the Hamiltonian of the compound system.
The value of the scattering matrix makes it possible to
determine the Hamiltonian; this is shown for cases in
which the compound system contains: (a) a finite number
of complex levels; (b) a continuous spectrum of complex
levels; (c) a degenerate real level. For all these
Card 1/2

USM/Theoretical Physics B-4
Abs Jour Referat Zhur - Fizika, No 5, 1957, No 10660
cases an explicit expression is written for the
HamiLtonian in terms of the parameters of the scattering
matrix; the Hami-Itonian is reduced to the simplest (tri-
angular) representation. Using the formulas derived, the
author considers the process of decay of the compound nu-
cleus under the condition that it has a continuous spec-
trum of complex levels. In conclusion, the method develo-
ped is generalized to include the case, when the particle
outside the nucleus is not free, but is in a certain poten-
tial field (for example, the Coulomb field of the nucleus).
The work is distinguished for clarity of presentation,
which, in spite of the mathematical complexity, makes it
accessible to the non-mathematician.
Card 2/2

Liv-SH IV,, F11
SUBJECT USSR PHYSICS CARD 1 / 2 PA - 1905
AUTHOR LIAIC,M.S.
TITLE On the Scattering Matrix of an Intermediary System.
PERIODICAL ])Okl.Akad Nauk,111, fasc.1, 67-70 (1956)
Issued: ; / 1~_57
The present work deals with deriving the not self-adjolned operator of the
energy of an intermediary system, which has been format on the occasion of
the elastic collisions of two particles. On this occasion the relativistic
dependence of the mass of these partizles on velocity is taken into account.
A close connection is found to exist between the scattering matrix and the
so-called characteristic matrix function of the corresponding not self-ad-
joined energy operator, so that it is in some cases possible to determine the
energy operator from the assumed scattering matrix. In thin connection the well-
known formula by E.P.VIIGNER and L.EISENBUD, Phys.Rov.72, 2~) (1947) is general-
ized for the case of the continuous spectrum of the intermodiary system. As an
example of application the energy operator for HEISFITBERG"3 model of elementary
particles is determined. In order to make the nature of this method quite clear,
only the elastic collisions between two uncharged particles a 1+a2 ---, C.-i a 2+a1
is studied in the present instance. Here C denotes the intermediary system. The
moment of momentum 1 and the spine of the particles shall be equal to zero.
The wave functions of the investigated system is beat represented in form of a
vector with two components. The HAMILTONIAN is accordingly written down as a
matrix of the second order. In order to take account of the relativistic de-
J 17 ' j

Dokl.Akad.Nauk,111,fasc.1,67-70 (1956) CARD 2 / 2 PA - 1905
pendence of the mass of the particles on velocity, representation in the momen-
tum space is adopted. Next, the matrix wave equation, which in separated into
two wave equations, is investigated. For the equation which determines the
state I of the intermediary gWe the following formula is eventually found:
H f_1V f. (a/2) /2)(V I+V2 1, fV2 P, For the scattering matrix we
21( R P I
find: S(W)- e- P/ 30M, so (W)- 1+ i((H* -WI)_1 1, 1). The function S o(w)
is called "characteristic function" of the operator H. The total probability P
of the intermediary system, which is referred to the time unit, is given by the
-1 1 f JPj 12
following expression: P (211,) Finally, the following
4-1
generalization of the formula by WIGNER and EIS NBUD is I, obtained:
S (V/)-(l+(iPt/2)q,(W))/(l-(iPT,/2),p(W)),(p(W)-((A-WI)-I 1 Here it holds
(b
that y(W) -)o dd(t)/(t-W), where is a not decreasing function. It
4 __P 4 -+ 1/2
is true that 10 M 1/(1,1) and E t denote the spectral family of the self-
adjoined operator A.
As an example the scattering function for the elastic collisions of two homoge-
neous particles are studied.
INSTITUTION: Hydrometeorological Institute, Odessa.

ti t T
SUBJECT USSR / PHYSICS CARD 1 / 2 PA - 1936
AUTHOR LIF910,M.S.
TITLE On the Intermediary System whinh is Formed on the Occasion of
the Scattering of Elementary Particles.
PERIODICAL Dokl.Akad.Nauk 1111faso-4, 799-802 0956)
Issued: 1 / 1~'5_77
The present work investigates the properties of an intermediary system formed
on the occasion of a collision betweem two elementary particles on the pre-
supposition that interaction between the particles is due to a quasioharge which
connects the corresponding fields. In this connection the expression SOM -
- (1+(iP/2),p(W))/(1 - (iP/2)y (W)) with ~ - c - 1 is used for the scattering
matrix of the collision of two particles a, t a2___) C --ip a2 + &V Here P de-
notes the total probability of the decay of the intermediary system, and for
1 -:~ -,p )
9(W) the equation V(W) - ((A-WI)- e 01 e0 applies. Here A denotes the self-ad-
joined operator for the energy f the id box", e - a certain coordi-
_!L~re
21 2 2'
nate vector, and W ij m + p + m + p m he total energy of the
system. 1 r 2 (ml >,-- 2) to
The author endeavors to find the amounts of P and T(W) by the example of the
scattering of a photon by an electron. On this occasion the electron "at first"
absorbs a photon with the fourdimensional momentum k2l and "afterwards" it emits
a photon with the fourdimensional momentum k". For this purpose the correspond-
2

Dokl.Akad.Nauk lll,,faso.4,799-802 (1956) CARD 2 / 2 PA - 1936
ing elements of the scattering matrix are written down in second approximation.
This scattering matrix is then transformed by transition'to new variables.
For the operator i-s"g-e nergy of the system described as a "covered box" we
2(W) - m 2 with M(W )12,e, a M m
find ip(W) __1/ V3_ 2 f -6,1621W , *mjjrm 2V42 i - 2*
For the construction of the operator A and the vector e 00 wave functions with
two components are introduced into the investigation. If the operator A and
the vector 7 are known the following equation can be found for the decay of the
intermediary 0 system 0: 1 df/dt-HI* f with HA f - Morf -(iP/2) (f,-e" )-e-" .
0 0
If the masses of both particles are different from zero, the operator A has a
continuous spectrum which fills the intervals: m, - m2,< ~ < mi + m2 and
_M 1 _M 21< ~'