Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## Wave dispersion in paramagnetic systems

### L.S. Kuz'menkov, S.G. Maksimov, V.V. Fedoseev

Moscow University Physics Bulletin 2000. 55. N 5. P. 1

A variance equation for natural modes in the "Pauli" paramagnetic systems has been found on the basis of equations of quantum hydrodynamics for a system of particles with spin. It has been shown that the index of refraction of transverse waves propagating along the external magnetic field depends explicitly on the magnetic susceptibility of a substance, which can be used for its measurement.

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## Effective rank of infinite-dimensional linear measurement model

### M.L. Serdobol'skaya

Moscow University Physics Bulletin 2000. 55. N 5. P. 5

The problem of effective rank (maximal dimensionality of measured signal estimate as a function of controlled root-mean-square estimation error) of an infinite-dimensional linear measurement model has been considered. An effective rank of the model, in which an instrument effect on the signal is described by an arbitrary linear bounded operator, has been found.

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## Effective action in $SU(2)$ gauge model with vortex

### V.Ch. Zhukovskii

Moscow University Physics Bulletin 2000. 55. N 5. P. 10

Effective potential of the $SU(2)$ gauge model with vortex in a 4-dimensional space-time has been calculated in a one-loop approximation. The minimum of the effective potential has been found.

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## Explicit solutions of equations of motion for one class of completely integrable classical four-particle systems in an external field

### D.V. Meshcheryakov, V.D. Tverskoy

Moscow University Physics Bulletin 2000. 55. N 5. P. 15

Explicit solutions have been found for one class of completely integrable four-particle systems in an external field. A formula has been derived that relate the initial conditions, coupling constant and the time of fall of two particles in interaction potential singularity.

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## Spectral problem for nuclear Coulomb potential

### O.S. Pavlova, D. Baskaran, A.R. Frenkin

Moscow University Physics Bulletin 2000. 55. N 5. P. 18

A discrete spectrum of the radial Schrodinger equation with a nuclear attractive Coulomb potential has been found employing the integral transformation method based on the Laplace transform of wave functions. The problem is reduced to searching for an approximate solution to an infinite system of linear algebraic equations. A spectrum of Schr$\stackrel{..}{o}$dinger's equation with the Yukawa potential for the state $S$ has been determined by means of the numerical calculations.

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## Integral equation method used in solving problems of waveguide bioinformatics

### V.P. Modenov, l.K. Troshina

Moscow University Physics Bulletin 2000. 55. N 5. P. 24

The influence of electrodynamic and geometrical characteristics of a biological object on the distribution of a scattered electromagnetic field has been studied by the waveguide electromagnetic probing method. The diffraction of the wave $H_{10}$ on the dielectric inhomogeneity simulating a biological object has been considered. The corresponding boundary problem for the Helmholtz equation has been solved by the method of integral equations with analytical regularization of its kernel.

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Atomic and nuclear physics

## Possibilities of utilizing photonuclear reactions to obtain energy in fission processes

### B.S. Ishkhanov, S.P. Likhachev, V.I. Mokeev

Moscow University Physics Bulletin 2000. 55. N 5. P. 30

To estimate the possibility of initiating nuclear chain reactions in subcritical assemblies by means of intense electron beams, we have calculated the neutrons yield from an $^{238}$U target as a result of the reactions $(\gamma,n)$, $(\gamma,2n)$ and $(\gamma,f)$ initiated by electron beams with energies of 10 and 30 MeV at a current of 100 mA. We have also calculated the ratio of the energy released as a result of the reaction $(\gamma,f)$ to the energy of the initial electron beam. We have demonstrated that the irradiation of the $^{238}$U target gives rise to neutron fluxes whose intensity is comparable to that of the fluxes in nuclear reactors.

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## Kinetic theory of low-frequency instability of gas-discharge plasma

### O.V. Kudrevatova$^1$, Meong-Khi Ri$^2$, A.A. Rukhadze$^2$

Moscow University Physics Bulletin 2000. 55. N 5. P. 35

Low-frequency instability of a de discharge in a weakly ionized plasma caused by the stimulated Cerenkov radiation of temperature relaxation "oscillations" by drifting electrons has been studied. The study has been conducted on the basis ofa kinetic equation involving the Bathnagar-Gross-Krook model collision integral allowing for the electron density and temperature relaxation.

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Optics and spectroscopy

## Unperturbing measurements of highly stable solid-state laser characteristics

### N. V. Kravtsov, S.V. Fetisov

Moscow University Physics Bulletin 2000. 55. N 5. P. 39

The possibility has been demonstrated of eliminating the effect of backscattering on the characteristics of highly stable solid-state lasers, as well as that of recording the laser output characteristics by the scattered pumping radiation and fluorescence radiation in the active element.

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Geophysics

## Reconstruction of altitude profiles of electron collision effective frequency in isotropic flat-layered ionosphere

### V.D. Gusev, E.G. Mikhailova, L.I. Prikhod'ko

Moscow University Physics Bulletin 2000. 55. N 5. P. 45

An inverse problem of reconstructing the altitude profiles of electron collision effective frequency in the ionosphere has been considered. In geometrical optics approximation, the problem is reduced to an Abel-type integral equation. The equation obtained has been analyzed numerically and an example of reconstruction of $\nu_{{\rm eff}}(z)$ for a parabolic ionospheric layer has been given.

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## Possibility of remote polarimetric investigation of electric field of the Moon

### V.I. Grigoryev, V.S. Rostovskii

Moscow University Physics Bulletin 2000. 55. N 5. P. 49

The possibilities of detecting the electric field set np on the Moon due to the baroelectric effect by the polarimetric methods are discussed.

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## Fractal dimensionality of ionospheric radio signals

### D.V. Kiryanov, N.V. Karabanov, D.I. Saponov

Moscow University Physics Bulletin 2000. N 5.

Experimental results are discussed of an investigation into the fractal properties of radio signals after being reflected from the nonuniform ionosphere of the Earth. Remote radio-sonde observation data have been processed using the wavelet analysis and an attractor reconstruction algorithm. The dimensionality values obtained for time realization of the Doppler frequency shift in an ionospheric radio signal provide data on fractal properties of nonuniform ionosphere on different scales.

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Theoretical and mathematical physics

## Study of characteristic equations for an electromagnetic wave propagating in the field of intense laser radiation according to the Born-lnfeld laws of electrodynamics

### V.I. Denisov, N.V. Kravtsov, E.G. Larionov, A.A. Zubrilo, V.B. Pinchuk

Moscow University Physics Bulletin 2000. 55. N 5. P. 59

In the Born-lnfeld nonlinear electrodynamics a weak electromagnetic wave is demonstrated to propagate in an intense field of laser radiation in a certain effective space-time, whose metric tensor depends on the electromagnetic field strength of laser radiation. The components of this tensor have been found.

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Atomic and nuclear physics

## Bremsstrahlung emission accompanying $\alpha$-decay of $^{210}$Po nucleus

### N.V. Eremin, S.V. Klimov, D.A. Smirnov, A.F. Tulinov

Moscow University Physics Bulletin 2000. 55. N 5. P. 62

The energy spectrum of bremsstrahlung accompanying the $\alpha$-decay of a $^{210}$Po nucleus has been measured. The probability of emission of bremsstrahlung photons decreases monotonically with an increase in their energy. The data obtained have been compared with the numerical results of calculation within the framework of the classical bremsstrahlung theory and quantum mechanical computation including the subbarrier region of $\alpha$-particle movement.

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## Measurement of low optical loss in liquids by "whispering gallery" modes resonator method

### E.N. Alyrzaev, M.L. Gorodetsky, V.S. Ilchenko, A.A. Savchenkov

Moscow University Physics Bulletin 2000. 55. N 5. P. 65

It has been demonstrated that low optical loss in liquids near a liquid-solid interface can be measured by the "whispering gallery" modes resonator (WGMR) method. This method was tested on some pure liquids and solutions. It has been found that the dependence of optical loss on ethanol concentration in water is described by the curve of a pronounced threshold shape.

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## Interference of radio oscillations with incommensurable frequencies

### N.V. Evdokimov, V.P. Komolov

Moscow University Physics Bulletin 2000. 55. N 5. P. 68

It has been demonstrated experimentally that the sign correlation of radio oscillations with proportionate incommensurable frequencies forms a dynamic chaos controlled by the delay of the constituent oscillations. This property can be useful in multichannel radio communication systems.

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Optics and spectroscopy

## Anisotropy of anisometric speckle structures

### Yu.V. Vasil'ev, A.V. Kozar', E.F. Kuritsyna, A.E. Luk'yanov

Moscow University Physics Bulletin 2000. 55. N 5. P. 72

It is found experimentally that a different degree of anisotropic roughness of narrow metallic strips leads to a marked difference in the character of inverse diffraction scattering of illuminating laser radiation. Anisotropy of the properties of originating random optical fields has been revealed.

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Solid state physics

## Origination of iron oxide nanoclusters on silicate glass formation

### A.A. Novakova, T.Yu. Kiseleva, I.V. Kovaleva

Moscow University Physics Bulletin 2000. 55. N 5. P. 76

A M$\stackrel{..}{o}$ssbauer study of Na$_2$O-CaO-SiO$_2$ glasses with low (up to 1%) content of iron enriched in the $^{57}$Fe isotope has been conducted. The structural and valence states of the Fe$^{2+}$ and Fe$^{3+}$ ions have been analyzed. A component with a characteristic magneto-relaxation shape observed in the spectra is indicative of the formation of ultrasmall Fe$^{3+}$ oxide clusters in glasses.

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Geophysics

## Effect of component composition on phonon heat transfer intensity in binary solid solutions of rockforming minerals

### G.I. Petrunin, I.A. Ilyin

Moscow University Physics Bulletin 2000. 55. N 5. P. 80

The nature of nonlinear dependence of lattice thermal conductivity of polyatomic binary solid solutions on their component composition has been studied using isomorphic series of plagioclases and synthetic garnets as an example. A variant of a theoretical relation has been proposed that adequately describes the experimental data.

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## Vertical structure of wind velocity at intense atmospheric convective vortex periphery

### E.P. Anisimova, A.M. Nikolaev, A.A. Speranskaya, 0.N. Chernyshev

Moscow University Physics Bulletin 2000. 55. N 5. P. 84

The authors discuss the results of studying altitude variations in the horizontal component of wind velocity at the periphery of atmospheric intense convective vortices (ICV) of tropical cyclone type. The study was made on model ICVs, some thermal hydrodynamic characteristics of which are similar to those of the lower troposphere in the central part of a tropical cyclone.

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