Faculty of Physics
M.V. Lomonosov Moscow State University

# Issue 3, 1970

## Gibbs-method calculation of trajectory probabilities for a brownian particle

### A.G. Baryshnikov

Moscow University Physics Bulletin 1970. 25. N 3. P. 1

A method is derived for calculating traiectory probabilities for a Brownian particle in configuration space and phase space on the basis of general principles of ibb's statistical mechanics. The method is freed of the usual theoretical limitations (i.e., a special form of the random process, a lack of correlation in the impulsive forces, etc.) and is applicable to various types of physical systems, including systems displaying an aftereffect. The method is illustrated for various examples of linear systems.

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## Study of mutual diffusion in the nb-zr system by local x-ray analysis

### G.N. Ronami, V.I. Gryzunov, E.M. Sokolovskaya, A.L. Tatarkina, and M.V. Raevskaya

Moscow University Physics Bulletin 1970. 25. N 3. P. 7

Mutual diffusion in the Nb-Zr system was studied with a Kameka MS-46 microanalyzer. The Dmu values were determined as a function of the Nb concentration, and the activation energies for mutual diffusion were calculated.

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## Mass spectrum of particles in nonlinear quark theory

### A.Kh. Bas'yuni and D.F. Kurdgelaidze

Moscow University Physics Bulletin 1970. 25. N 3. P. 10

Equations are derived for the mass spectrum of baryons and mesons within the framework of nonlinear quark theory on the basis of the relativistic, SU(3)-invariant equations derived previously for these particles. The equations derived are the same as those found by the ordinary (purely group) approach in nonrelativistic SU(6)-invariant theory.

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## Thermal fluctuations in the amplitude of surface-charge waves in a partially filled plasma waveguide

### Рак Quan Ir

Moscow University Physics Bulletin 1970. 25. N 3. P. 15

Thermal fluctuations in the amplitude of surface-charged waves are analyzed for a partially filled plasma waveguide of circular cross sections. A dispersion equation is found for the surface-charged waves.

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## A canonical system of variables in the theory of satellite motion

### A.A. Orlov

Moscow University Physics Bulletin 1970. 25. N 3. P. 17

A method involving variation of arbitrary constants is used to solve the differetial equations for intermediate non-Kepler motion. A new system of canonical variables is introduced which is convenient for studying perturbations of this motion.

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## Choice of metrics for the reference frame in the three-dimensional chronometrically invariant two-metric formalism

### V.A. Barynin

Moscow University Physics Bulletin 1970. 25. N 3. P. 22

The choice of temporal and spatial metrics for the reference frame in the three-dimensional chronometrically invariant two-metric formalism is discussed in connection with various approaches for describing gravitation.

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## Some exact solutions of the dirac equation

### V.G. Bagrov, I.M. Ternov, В.V. Kholomai

Moscow University Physics Bulletin 1970. 25. N 3. P. 24

Variables are separated in the Dirac equation for an electron moving in a uniform magnetic field and in a parallel, time-dependent electric field. Explicit solutions are fo\Dld for certain particular fields.

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## Radiation by a particle in a low-lying energy level in a strong magnetic field

### M.M. Mkrtchyan

Moscow University Physics Bulletin 1970. 25. N 3. P. 29

Equations are derived for the total power and the polarization of the radiation emitted by an electron or by a scalar particle in the second excited state and moving in a superstrong magnetic field.

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## Effect of electric-field perturbations near the anode on the oscillations on a penning discharge

### G.V. Smirnitskaya, E.M. Reikhrudel, and I.A. Nosyreva

Moscow University Physics Bulletin 1970. 25. N 3. P. 32

In an attempt to determine the nature of the oscillations which arise in a Penning discharge, a study has been made of the role played by perturbations caused in the electric field near the anode by longitudinal apertures in the cylindrical anode. The radial potential drop was measured by the "ion-kinetics" method. A study was also made of the sensitivity of the discharge oscillations to the potential on probes placed in the anode apertures.

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## Bremsstrahlung during the scattering of a neutrino by an electron with an account of radiation corrections

### В.K. Kerimov and V.P. Tsvetkov

Moscow University Physics Bulletin 1970. 25. N 3. P. 38

The angular and energetic distributions are calculated for the bremsstrahlung emitted during the scattering of a neutrino by an electron. The radiation corrections of order α to the effective total cross section for these scattering is calculated; the expression for this correction also takes into account the emission of a hard photon.

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## Frequency correlations in the fluctuations of spherical waves propagating in a turbulent medium

### V.A. Eliseevnin

Moscow University Physics Bulletin 1970. 25. N 3. P. 43

The frequency correlations are calculated for the amplitude and phase fluctuations of two spherical waves of different frequencies propagating in an isotropic turbulent medium. The structure function of the refractive index of such a medium obeys a Kolmogorov-Obukhov two-thirds law. The analysis is carried out from the wave point of view in the first approximation of the smooth-perturbation method.

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## Root-trajectory study of two-dimensional systems having antisymmetric cross coupling

### G.A. Bendrikov, V.I. Ogorodnikova, and N.A. Sukhacheva

Moscow University Physics Bulletin 1970. 25. N 3. P. 51

The basic properties of the root trajectories, which can be used for qualitative and quantitative of the dynamics of identical two-dimensional systems, are studied for characteristic equations of the form N(p) + jaM(p)= 0 with complex coefficients. Geometric and analytic methods for constructing these root trajectories are described. The degree of the trajectory equation in ω^2 is much lower than that of the characteristic equation, so it becomes easier to analyze two-channel systems described by high-order differential equations. Illustrative constructions of root trajectories are described.

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## Second-order secular perturbations in the motion of a remote satellite

### V.P. Dolgachev

Moscow University Physics Bulletin 1970. 25. N 3. P. 57

Equations are derived for the second-order secular perturbations in the orbital elements for remote earth satellites under the condition that the perturbing function contains terms of third degree in the Lagrange variables.

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## Radiation polarization of slightly relativistic electrons in a magnetic field

### D.V. Gal'tsov and N.S. Nikitina

Moscow University Physics Bulletin 1970. 25. N 3. P. 63

In an analysis of the effect of external electromagnetic radiation on the spin state of slightly relativistic electrons in a uniform magnetic field, it is shown that an electron beam can become highly polarized under certain conditions. An expression is found for the probability for radiative transitions involving spin flipping which holds for all particle energies.

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## Optical breakdown in a gas mtxture

### E. Gernits, R.M. Minikaeva, V.E. Mitsuk, and V.A. Chernikov

Moscow University Physics Bulletin 1970. 25. N 3. P. 67

## Energy of fast electrons in a gas discharge at a pressure of $10^(-2)—10^(-3)$torr

### A.I. Krokhina

Moscow University Physics Bulletin 1970. 25. N 3. P. 69

## Thermal properties of tantalum at high temperatures

### A.V. Arutyunov, I.N. Makarenko, L.N. Trukhanova, and L.P. Filippov

Moscow University Physics Bulletin 1970. 25. N 3. P. 71

## Oscillations of nonlinear systems affected by small random perturbations

### В.V. Aleshin

Moscow University Physics Bulletin 1970. 25. N 3. P. 73

## Absolute perturbations in the motions of juno due to all the major planets

### M.P. Boris

Moscow University Physics Bulletin 1970. 25. N 3. P. 76

## Effect of ionic ordering on the magnetic properties of nickel chromite ferrite

### A.N. Goryaga and L.P. Mitina

Moscow University Physics Bulletin 1970. 25. N 3. P. 78

## Petrov classification of gravitational fields and chronometric invariants

### R.F. Polishchuk

Moscow University Physics Bulletin 1970. 25. N 3. P. 80

## Chronometrically invariant formulation of the second law of relativistic thermodynamics

### Kh. K. Del Prado Segura

Moscow University Physics Bulletin 1970. 25. N 3. P. 83