Faculty of Physics
M.V.Lomonosov Moscow State University

## Temperature dependence of the Raman-scattering intensity in quartz crystals with artificially introduced defects

### L.P. Osipova, M.A. Smirnova, M.V. Novakovskaya

Moscow University Physics Bulletin 1984. 39. N 1. P. 1

It is established that the temperature dependence of the Raman-scattering intensity in synthetic quartz irradiated by fast neutrons (with no alluminum impurities or the corresponding color centers) is anomalous, as in natural irradiated crystals including aluminum defect tetrahedra. It is suggested that amplification of the anharmonicity of the lattice vibrations of the crystal is associated with the formation of a large amount of structural point defects (and corresponding color centers) of nonimpurity type under the action of fast neutrons.

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## Cluster hypernuclei

### N.N. Kolesnikov, V.A. Kopylov, A.V. Kolesov

Moscow University Physics Bulletin 1984. 39. N 1. P. 6

Multiparameter variational calculations of the hypernuclei $^9_{\Lambda}Be (\alpha+ \alpha + \Lambda)$ and $^1_{\Lambda \Lambda}Be (\alpha +\alpha +\Lambda + \Lambda)$ and the quasi-molecular hypernuclear system $\alpha - \Lambda - \alpha$ with parallel orientation of the deuteron spins are performed with semirealistic potentials. The clustering effect in hypernuclei is investigated, as well as the influence of the form of the $\Lambda \Lambda$ potential on the binding energy of the double hypernuclei.

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## Five-dimensional approaches and the theory of the hydrogen atom

### Yu.S. Vladimirov, V.V. Kislov

Moscow University Physics Bulletin 1984. 39. N 1. P. 11

The O(4) symmetry of the Schr$\stackrel{..}{o}$dinger equation for the hydrogen atom discovered by Fock, is discussed. The difficulties of physical interpretation of the result using the Fock procedure for determining the stereographic projection in momentum space is indicated. A generalization of the stereographic projection is suggested such that the O(4) symmetry of the hydrogen atom has a clear physical interpretation within the framework of a unified five-dimensional theory of gravitation, electromagnetism, and charged matter. In passing, the problem of the form of the dependence on the fifth coordinate in the given theory is solved.

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## Interaction of gradient flow with the density-discontinuity layer

### N.K. Shelkovnikov, S.M. Novochinskii

Moscow University Physics Bulletin 1984. 39. N 1. P. 19

The model of a two-layer liquid is employed in investigating the features of circulation in the tidal region, the spatial variability in the structure of the density-discontinuity layer, in the presence of velocity shear and pressure gradient, and also the entrainment of denser liquid from the lower to the upper layer.

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## New proof of the convergence of the Laplacian series at physical surfaces of the planets

### N.A. Chuikova

Moscow University Physics Bulletin 1984. 39. N 1. P. 24

It is proven that the external gravitational potential of a planet may be written as a series in spherical functions - $V(r,\phi,\lambda)=f \sum_{n=0}^{\infty} \frac{1}{r^{n+1}}\int \mu (r’,\phi’, \lambda’)P_n(cos \gamma)r’^{n+2} dr’ d sin \phi’ d\lambda’$, uniformly converging everywhere on and outside the physical surface of the planet, with a normalized nonlinear dispersion of the relief height conforming to the condition $\bar{D}_J<\frac{1+\hat{H}/R}{\beta J \sqrt{2 J+1}}\left( \frac{R-\Delta}{R+\hat{H}} \right)^J$, where $\Delta>0$ is the maximum depth of the relief with respect to the mean sphere radius R; $\hat{Н}$ is the height; the density of the surface masses (lying above the sphere passing through the observation point $r, \phi, \lambda$) is an analytical function of the coordinates.

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## Canonical-transformation method in the problem of potential scattering

### Yu.G. Pavlenko

Moscow University Physics Bulletin 1984. 39. N 1. P. 31

It is shown that the formulation of the scattering problem in canonical variables significantly simplifies the calculations and allows universal integration methods based on the theory of canonical transformations to be used.

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## Reconstructing a surface with near-Lambert optical properties from a stereographic pair

### A.L. Antsiferov, Yu.P. Pyt'ev

Moscow University Physics Bulletin 1984. 39. N 1. P. 37

A model of the formation of images of Lambert surfaces and those with near-Lambert optical properties is considered. The possibility of identifying points on stereographic photographs which are images of a single point of the surface is noted, and a method is proposed. The problem of reconstructing a surface with near-Lambert optical properties from a stereographic pair is considered.

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## Choice of coupling parameters in frequency-stabilizing systems

### I.I. Minakova, S.A. Lebedinskii

Moscow University Physics Bulletin 1984. 39. N 1. P. 42

The results of theoretical calculation of the dynamic characteristics of a self-oscillatory system with different types of coupling between the loops are given; conditions with minimum stability are determined, and the corresponding losses in stabilization are estimated as a function of the regeneration capacity.

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## The basic algebraic laws of dipole combinations of dipoles and regular sequences of these combinations

### V.I. Shestakov

Moscow University Physics Bulletin 1984. 39. N 1. P. 47

The basic algebraic laws of dipole combinations are taken to be such that any set of DP satisfying these laws is an Abelian semigroup relative to the operations of parallel and series combination of DP. A characteristic feature of this algebra is that a neutral element of any of these semigroups plays the role of an all-absorbing element of another one. From the basic laws of this algebra, analogous laws of the algebra of regular sequences of dipole combinations of dipoles may be deduced. For neutral and all-absorbing elements of each of the two semigroups considered, the algebra investigated is found to be Boolean. An analogous assertion is also valid for the algebra of regular sequences of dipole combinations of DP.

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## Synchrotron radiation of electrons in inhomogeneous magnetic fields. The case of azimuthal inhomogeneity

### V.Ch. Zhukovskii, O.E. Shishanin

Moscow University Physics Bulletin 1984. 39. N 1. P. 55

The influence of induced oscillations on the characteristics of synchrotron radiation is considered. Formulas that are accurate to the first quantum correction are obtained for the intensity of components of the linear polarization of the radiation, taking account of both betatron and induced oscillations of the electron beam. It is noted that distortion of the magnetic median surface must be taken into account in experiments with synchrotron radiation.

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## Band properties of the spectral characteristics of laminar media

### A.V. Tikhonravov

Moscow University Physics Bulletin 1984. 39. N 1. P. 60

Estimates of the spectral characteristics of single-mode waveguides are obtained as a function of the parameters characterizing the smoothness of the wave resistance of the inhomogeneous section of the waveguide and length of this section. It is shown that these estimates allow a priori concepts to be obtained regarding the realizability of the band properties of waveguides required in synthesis.

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## Solution of the two-dimensional magnetotellurgic problem using Tikhonov regularizing algorithms

### V.B. Glasko, N.I. Ol'khovskaya

Moscow University Physics Bulletin 1984. 39. N 1. P. 65

It is shown that the general Tikhonov regularizing algorithm applies to the case of a model in which the conduction of the terrestrial core is approximated by smooth functions. The magnetotelluric problem is formulated for a special case of the local conduction distribution: $\sigma(x, z) = \sigma_1(x)\sigma_0(z)$. Using a regularizing algorithm, a mathematical experiment is performed to determine the horizontal inhomogeneity of the geoelectric discontinuity.

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## Light-beam scanning in para-tellurite crystals

### Z.T. Azamatov, I.B. Belikov, V.B. Voloshinov, F.D. Mamatdzhanov, V.N. Parygin

Moscow University Physics Bulletin 1984. 39. N 1. P. 70

Light diffraction on ultrasound in the para-tellurite crystal is investigated. For acoustic waves in the frequency range 8.8$\div$80.0 MHz, the Bragg angles of incidence of the optioal beam at the ultrasound is measured. In the frequency range 30.0$\div$50.5 MHz, scanning of the light beam in the first diffractional order is performed, with a diffraction efficiency of 40$\div$80% at a controlling electric power of 120 mW. The features of the scanning are investigated by means of double light scattering on ultrasound. The reflector resolution measured for para tellurite $N=330\pm20$ differs from the calculated value N = 400 by 10-20%. The influence of thermal perturbations on the acoustooptical cell is qualitatively estimated.

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## Distribution of the gravitational force and plumbline deflections on the surface of Mars

### T.G. Maksimova, N.A. Chuikova

Moscow University Physics Bulletin 1984. 39. N 1. P. 77

It is proposed to use, as a reference surface, the smoother physical surface of Mars, which is an expansion with respect to normalized spherical functions to the 16-th power. The coefficients of the expansion are determined on the basis of the coefficients of the expansion of the relief and the gravitational potential to the 12-th power. Pictures of the variation in gravitational force with respect to $g_0$ = 372.69 Gal and plumbline deflection at the smoothed physical surface are given.

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## Field asymptote of a vertex function

### Yu.M. Loskutov, V.V. Skobelev

Moscow University Physics Bulletin 1984. 39. N 1. P. 84

By summing diagrams of ladder type, the asymptote of a vertex function in a superstrong magnetic field is found. It is shown that the field vertex contributions to the matrix elements are small in comparison with the corresponding contributions of the mass and polarization operators.

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## New class of static spherically symmetric solutions of the Einstein equations in the presence of matter. I

### Yu.N. Vlasenko, P.I. Pronin

Moscow University Physics Bulletin 1984. 39. N 1. P. 89

A new method of obtaining internal static solutions of the Einstein equations is proposed and used to find a series of solutions for spherically symmetric configurations. The matching conditions with the external Schwartzschild solution are considered.

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## Accurate solutions of the Dirac equations in a quantized pseudoscalar wave

### V.R. Khalilov, V.K. Perez-Fernandez

Moscow University Physics Bulletin 1984. 39. N 1. P. 95

Accurate solutions of the Dirac equation are obtained, describing a nucleon doublet in the classical field of a plane pseudoscalar wave, against the background of which there are single-mode quantum excitations.

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## Parametric generation in an oscillatory loop with discontinuously changing parameters

### V.P. Komolov, D.A. Tishchenko, P.N. Shashkov

Moscow University Physics Bulletin 1984. 39. N 1. P. 102

The conditions of parametric excitation of oscillations in a loop with discontinuously changing parameters determining the relations between the durations of residence of the loop in discrete states and the parameter values in these states are described. It is shown that such a loop has a set of excitation modes of oscillations of different form. The results of experimental investigation of the balance parametric loop with discontinuously changing capacitance, in which 16 generation regions were observed, are presented.

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## Regions of excitation of oscillations in a loop with discontinuous capacitance modulation

### V.P. Komolov, D.A. Tishchenko, P.N. Shashkov

Moscow University Physics Bulletin 1984. 39. N 1. P. 106

Relations for the limits of the regions of excitation of oscillations in a loop with discontinuous modulation of the capacitance are describied; the relations are obtained on the basis of analysis of the stability of the solution of the corresponding Hill equation. It is shown that the excitation zones may be divided into discrete regions; the number of these regions does not exceed the number of zones and depends on the parameters of the modulating perturbation. Results are given of an experimental investigation of the excitation of a parametric loop with rectangular videopulse pumping, with a depth of capacitance modulation varying within the range 0$\div$0.6.

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## Mathematical model of the mean-velocity profile of a benthic density current

### A.Yu. Pyrkin

Moscow University Physics Bulletin 1984. 39. N 1. P. 110

A two-dimensional steady turbulent benthic density current with a specified density profile is considered. The solution of the equations in the approximation of constant turbulent viscosity over the vertical is in good agreement with experimental results.

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## Estimating the components of the water-air heat flux in laboratory investigations

### V.N. Aksenov, E.G. Andreev, I.D. Bakanov

Moscow University Physics Bulletin 1984. 39. N 1. P. 113

Results are given of laboratory investigations of the heat-flux components close to the water-air interface with various values of the temperature difference between the media. The estimates presented are useful for more correct modeling of the full-scale conditions of heat transfer in laboratory experiments.

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## Structure of strong shock waves in argon

### Sufian Aslam, A.P. Ryazin

Moscow University Physics Bulletin 1984. 39. N 1. P. 116

The change in structure of a shock wave (SW) in argon with increase in its intensity is investigated experimentally for initial pressures of 3 and 25 torr and velocities in the ranges 6-8.5 and 3.5-6.2 km/sec. It is established that two different SW structures exist, as well as a transitional region in which the SW structure is unstable.

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## Kinetics of the dissociation of diatomic molecules with laser excitation of low vibrational levels and effective heat extraction

### S.G. Grebenyuk, A.I. Osipov

Moscow University Physics Bulletin 1984. 39. N 1. P. 119

The influence of the initial conditions and form of the exciting pulse on the kinetics of dissociation is analyzed over the whole time interval from the initial stages to the establishment of steady conditions. It is shown that the initiation of dissociation by external radiation is more favorable at low translational temperatures than at high temperatures, and an exponential form of the pumping pulse is most effective here.

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## Quantum chromodynamics and the quasi-classical approximation

### M.K. Ermolaev, N.F. Nelipa

Moscow University Physics Bulletin 1984. 39. N 1. P. 123

An expression is obtained for the amplitude of quantum chromodynamics in the quasi-classical approximation.

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## Statistical characteristics of random signals in a nonlinear medium

### A.S. Gorshkov, L.G. Lyashed'ko, I.T. Trofimenko

Moscow University Physics Bulletin 1984. 39. N 1. P. 127

Theoretical and experimental results for the variation in distribution function of a narrow-band noise signal propagating in a nonlinear weakly dispersive medium are compared. Dissipation smooths the nonlinear distortions of the distribution function, and cubic nonlinearity leads to asymmetry.

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## Wavefront control of optical radiation propagating in a medium that moves at variable velocity

### V.A. Trofimov

Moscow University Physics Bulletin 1984. 39. N 1. P. 130

Compensation of the distortions of optical radiation passing through a nonlinear layer of a medium which is moving at variable velocity is considered. The stability conditions and modes of development of the initial slope of the beam wavefront are determined.

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## Limiting efficiency of plasma amplifier

### V.K. Grishin, M.F. Kanevskii

Moscow University Physics Bulletin 1984. 39. N 1. P. 133

The efficiency of the interaction of a charged beam with an excited electromagnetic wave is investigated. It is shown that the limiting efficiency of a plasma amplifier is 0.5. The method proposed may be used for estimates in various electrodynamic structures.

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## Special Legendre transformation of generating functionals in the case of SU(2) symmetry

### A.P. Demichev

Moscow University Physics Bulletin 1984. 39. N 1. P. 136

The second Legendre transformation of the generating functional is considered for Green's function with respect to some of the bilocal currents realizing an irreducible representation of symmetry groups of the Lagrangian. It is shown that diagrammatic expansion of the functional obtained is of two-particle-reducible type.

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