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

## Calculating deeply inelastic diagram asymptotics with vector mesons in an exchange channel in a range of low $х$ in a Feynman calibration

### N.I. Usyukina

Moscow University Physics Bulletin 1986. 41. N 4. P. 1

Twice logarithmic asymptotics of diagrams from the perturbation theory with vector mesons are examined using integral representations and Mellin expansions in an exchange channel in a deeply inelastic range at low values of $x$ in a Feynman calibration.

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## On the criterion of resonance overlap and deformation of separatrices

### P.V. Elyutin

Moscow University Physics Bulletin 1986. 41. N 4. P. 8

For two-dimensional images which preserve a surface, a method is indicated for building the skeleton of the separatrix which does not use the smallness of nonlinearity. It is shown in an example of a standard image that near the boundary of global stochasticity the deformation of the separatrix is comparable with the width of the stochastic layer and is substantive in the criterion of resonance overlap. A two resonance model, for which an above stochasticity threshold evaluation is acquired which is in agreement with the results of computer experiments, is also examined.

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## A certain model of formation of a fractal dimensionality in the Schroedinger problem

### V.L. Bonch-Bruevich

Moscow University Physics Bulletin 1986. 41. N 4. P. 13

The types of solutions which form in a one-dimensional nonlinear problem about interaction between electrons and acoustical phonons are investigated. Conditions at which the multitude of solutions ia found to be fractal are indicated.

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## Increasing the resolution of diffusion-type devices

### S.S. Zadorozhnyi, A.A. Kozlov, Yu.P. Pyt'ev

Moscow University Physics Bulletin 1986. 41. N 4. P. 17

The problem of increasing the resolution of diffusion type devices is examined on an example of a pO$_2$ sensor - a meter for measuring the partial oxygen pressure used in biological investigations. A concept of resolution of the measurement device and the measurement-computer complex is formulated. A mathematical model of the pO$_2$ sensor is built. The problem of reducing the data acquired on the output of the sensor to a form which it would have on the output of a device with higher resolution is solved.

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## One problem of structural diagnostics

### V.B. Glasko, A.Yu. Gubar, E.V. Fedotov

Moscow University Physics Bulletin 1986. 41. N 4. P. 22

A one-dimensional model of the problem about determining the structural characteristics of a medium using an ultrasonic probing method is examined. The question about the uniqueness of solution of the problem is investigated. Asymptotic analysis is used to establish which types of characteristics of the structure may be acquired by the cited method in the high frequency range with an assigned experimental precision.

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## Limitation on the vertex constant in a dispersion approach and the radius of the nonperipheral part of interaction

### A.N. Safronov

Moscow University Physics Bulletin 1986. 41. N 4. P. 33

A new limitation on the vertex constant, which may be used for extracting information about the radius of the nonperipheral part of interact ion, is acquired on the basis of a dispersion approach. The method id used for analyzing the $s$-wave $nd$-scattering in a doublet state.

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## Limitation in the spectrum of modulationally unstable Langmuir waves in a relativistic plasma

### A.S. Vakhdeyn (People's Democractic Republic of Yemen), L.S. Kuzmenkov, O.O. Trubachev

Moscow University Physics Bulletin 1986. 41. N 4. P. 106

A nonlinear dispersion relation is acquired for Langmuir waves in a relativistic plasma, whose phase velocities are similar to the speed of light. It is shown that only waves with supersonic phase velocities will be modulationally unstable at $T_{e} \geq m_{e}c^{2}$.

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## Equations of state of a thermodynamic system and a regularization method

### I.P. Bazarov, P.N. Nikolaev

Moscow University Physics Bulletin 1986. 41. N 4. P. 110

A method is proposed for determining the thermodynamic functions from known asymptotic data. A regularization method with a quasi-optimal regularization parameter is used.

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Atomic and nuclear physics

## Coulomb break-up of an antideuteron atom

### D.E. Kharzeev, A.A. Khrapov

Moscow University Physics Bulletin 1986. 41. N 4. P. 27

The break-up of an antideuteron in a Coulomb nuclear field, which results in escape of an antineutron and the formation of an antiproton atom, is examined. In calculating the probability of Coulomb break-up, all of the orbits of the antiproton were considered, including even the noncircular orbits. A convolution type optical potential is built to describe the competing process of absorption of the antideuteron by the nucleus. It is discovered that the Coulomb break-up dominates over strong absorption for nuclei with any values of Z.

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## The effect of the anomalous magnetic moment of a neutron on beta-decay in an electromagnetic wave field

### I.M. Ternov, O.S. Pavlova, V.N. Rodionov, A.E. Lobanov, O.F. Dorofeev

Moscow University Physics Bulletin 1986. 41. N 4. P. 38

The effect of an electromagnetic wave on the initial state of a neutron during beta-decay is examined on the basis of the use of precise solutions of movement equations of neutral particles caused by magnetic moment. A relativistic calculation is performed of the probability of the process, and the contribution caused by the anomalous magnetic moment of the neutron is identified.

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## Dependence of the survival fraction of reflected molecular ions on the mutual disposition of atomic rows on the surface of a crystal

### L.L. Balashova

Moscow University Physics Bulletin 1986. 41. N 4. P. 113

A comparative analysis is performed of the orientational effects with reflection of molecular nitrogen ions with an energy of 30 keV from the (100) and (110) facets of a copper crystal. It is established that the nature of the characteristics of the survival fraction is not a function of the crystallographic direction, but is determined by the nature of the mutual disposition of the atomic rows on the surface of the crystal.

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## A combined surface wave relativistic generator

### N.A. Garutsa, V.I. Kanavets, A.I. Slepkov

Moscow University Physics Bulletin 1986. 41. N 4. P. 43

The nature of energy exchange between a stream and a field in a surface wave generator is theoretically investigated in a high current relativistic electron stream with an electron energy of $\varepsilon_{0}=1$ MeV. It is shown that in systems which consist of sectors of smooth waveguides with periodic heterogeneities and transverse dimensions much greater than the working wavelength with the use of interaction between the stream and a field with a lower axially symmetrical mode at frequencies near the boundary of the transparency band it is possible to acquire an effect of cyclotron power amplification and an electron efficiency of interaction greater than 40%.

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## Toward a linear theory of high current dielectric amplifiers using relativistic electron beams

### A.F. Aleksandrov, M.V. Kuzelev, O.E. Pyrkina

Moscow University Physics Bulletin 1986. 41. N 4. P. 116

An idealized model - a uniform dielectric waveguide permeated by a dense, magnetized electron beam - is examined. It is found that an increase in the beam current results in a narrowing of the amplification zone and its shift into a frequency range greater than the resonant. At the same time the Compton mode of operation of the amplifier shifts into a Raman mode or into an anomalous Doppler mechanism. The dependence of the amplification coefficient on the misalignment of the frequency at different values of the beam current is cited.

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Optics and spectroscopy

## The effect of mode locking on interaction between counter propagating waves in a solid-state ring laser

### E.L. Klochan, E.G. Lariontsev

Moscow University Physics Bulletin 1986. 41. N 4. P. 50

A system of equations is acquired for the parameters of ultrashort light pulses (USP) in a solid-state ring laser with active mode locking which considers the interaction of counter propagating USP due to inverse reflections in a modulator. The mode of capture of the frequencies of the counter propagating waves is investigated. It is shown that with specific phases of scattering coefficients on the faces of the modulator and with specific modulator lengths, it is possible to eliminate suppression of the counter propagating waves which form with an increase in the misalignment of the modulation frequency relative to its optimal value.

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## Coherent effects in saturation spectroscopy

### S.Yu. Nikitin

Moscow University Physics Bulletin 1986. 41. N 4. P. 55

A method from the perturbation theory is used to investigate coherent effects in saturation spectroscopy of combinationally active transitions associated with perturbation of the populations of quantum levels under the effects of weak probing waves.

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## Diffraction theory of a multibeam interferometer

### A.V. Belinskii, A.S. Chirkin

Moscow University Physics Bulletin 1986. 41. N 4. P. 62

Multibeam interferometers are widely used in optical spectroscopy and quantum electronics. However, in examining the properties, their mirrors are assumed to be infinite, as a rule. In this work a theory of multibeam interferometers is developed with consideration of the phenomenon of diffraction, where a modal approach is used. An expression is found for the mode transmission coefficient. The developed theory makes it possible to evaluate the effect of finite dimensions of the mirrors of the interferometer and the illuminating beam on the effectiveness of transformation of the latter.

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## Approximating the absorption band shape of associated dye molecules

### V.I. Yuzhakov, V.M. Boitsov

Moscow University Physics Bulletin 1986. 41. N 4. P. 68

A method is proposed for describing the shape of the absorption band of associated dye molecules. The calculations are performed for associates of rhodamine 6Zh at different temperatures. No dependence of the half widths of the relaxation component or the characteristics of nonuniform expansion of the spectra of the associates on temperature are discovered.

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## Diagnosing vibrational states of multiatomic molecules using the integral intensity of overtone and component frequency fluorescence

### E.N. Martynova, V.T. Platonenko, N.A. Sukhareva

Moscow University Physics Bulletin 1986. 41. N 4. P. 72

A theoretical investigation is performed of the possibility of using nonlinear infrared-fluorescence for diagnosing the vibrational states of multiatomic molecules. A method is justified for measuring the absolute vibrational temperatures and for determining the degree of imbalance of the intramodal and intermodal energy distributions through the relation of the integral intensities of fluorescence of overtones and component frequencies.

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## Numerical analysis of the vibrational kinetics of СО$_2$ coupled modes

### A.I. Odintsov, A.I. Fedoseev, L.A. Fomenko

Moscow University Physics Bulletin 1986. 41. N 4. P. 78

Calculations are performed of the dynamics of formation and the type of quasi-stationary distributions (QD) of vibrational populations of levels of coupled modes in imbalanced carbon dioxide. In typical conditions the establishment of QD occurs over a time which corresponds to $\sim 10^{2}$ of the gas kinetic collisions. The qualitative differences in the acquired QD from Treanor distribution are revealed.

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## The effect of resonant radiation capture on polarization of the active medium of gas lasers

Moscow University Physics Bulletin 1986. 41. N 4. P. 119

Polarization of the active medium of a gas laser is calculated on the basis of a system of quantum kinetic equations for density matrix elements with consideration of radiation capture. A precise expression for the actual and imaginary parts of complex polarizability is acquired within the cited approximation. The results are valid for arbitrary fields and for any relations between the relaxation constants. It is shown that capture may noticeably affect the size of the complex polarizability.

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## Generation of a second harmonic and a total frequency with reflection from a silicon surface implanted with phosphorus ions: diagnosis of crystalline structure randomization

### M.F. Galyautdinov, S.V. Govorkov, N.I. Koroteev, I.B. Khaibullin, I.L. Shumai

Moscow University Physics Bulletin 1986. 41. N 4. P. 123

Observation of orientational relations of the intensity of the second harmonic and the total frequency generated with reflection from the (111) cut of a silicon surface implanted with phosphorus ions is reported. The experiment showed that a rise in the implantation dose results in a drop in the relative value of the anisotropic contribution to the signal, which corresponds to a gradual rise in the degree of randomization of the crystalline structure.

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## Pulsed optical effects on near-electrode processes

### P.V. Kozlov, E.K. Kozlova, A.I. Portnyagin

Moscow University Physics Bulletin 1986. 41. N 4. P. 127

The characteristics are studied of the behavior of electrode potential with pulsed optical effects on an electrochemical cell when a simultaneous displacement of the thermal, chemical, and electrical equilibrium occurs on the metal and electrolyte interface. It is discovered that the surge in potential reaches 0.5-0.6 V. The times it takes for the system to lose equilibrium and to return exceed the laser pulse duration by several orders of magnitude.

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Geophysics

## Velocity and temperature profiles in a cold film near the free surface of a plane-parallel stream of water

### O.N. Melnikova, G.G. Khundzhua

Moscow University Physics Bulletin 1986. 41. N 4. P. 85

A technique is developed for determining the vertical profile of the mean velocity of a stream in an upper millimetric layer. The results are cited of a synchronous measurement of the velocity and temperature in a laboratory stream. It is explained that the upper part of a cold film with a thickness of several tenths of millimeters is a laminar sublayer with a linear velocity and temperature profile. The thickness of the sublayer is reduced with a rise in the velocity of the stream, while the gradients of velocity and temperature are increased.

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Solid state physics

## Magnetization and magnetostriction of NiFe$_{2-x}$Sc$_x$O$_4$ spinels

### K.P. Belov, N.V. Volkova, Subkhi Bekhiam Naval (Iraq), G.Ya. Ageeva

Moscow University Physics Bulletin 1986. 41. N 4. P. 90

The specific magnetization and the constants of magnetostriction $\lambda_{100}$ and $\lambda_{111}$ of three monocrystals of the system NiFe$_{2-x}$Sc$_x$O$_4$ (x = 0,05; 0.12; and 0.3) are measured in a temperature range of 4.2 K to the Curie point. An anomalous increase in the constants $|\lambda_{100}|$ and $|\lambda_{111}|$ is observed in a temperature range from 77 to 4.2 K. The concentration relation of $\lambda_{111}(x)$ is linear at all temperatures, while that of $\lambda_{100}(x)$ is linear at room temperature but is not linear at lower temperatures.

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## On the theory of magnetooptical phenomena in amorphous alloys of transition metals

### A.V. Vedyaev, A.B. Granovskii, M.Kh. Usmanov

Moscow University Physics Bulletin 1986. 41. N 4. P. 95

The high frequency Hall conductivity of amorphous magnetically ordered alloys is calculated in an approximation of a Feber-Zeeman model. Expressions are acquired for the intraband magnetooptical absorption in the infrared range of the spectrum. It is shown that consideration of scattering in the structural disorder leads to a great difference in the temperature and concentration relations of the magnetooptical effects from the case of crystalline alloys of transition metals.

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## X-Ray identification of the deformation tensor in Bi monocrystals and Bi$_{1-x}$Sb$_x$ $(x \leq 0,1)$ alloys with strong anisotropic deformation in annular rings

### A.L. Ilinskii, O.L. Isakova, M.Yu. Lavrenyuk, N.Ya. Minina

Moscow University Physics Bulletin 1986. 41. N 4. P. 100

All of the components of the tensor of deformation of $\varepsilon_{ij}$ are acquired using a method of X-ray diffractometry at liquid nitrogen temperature and the nature of the stressed state of samples of monocrystalline Bi and Bi$_{1-x}$Sb$_x$ $(x \leq 0,1)$ alloys, deformed in annular rings using a method which has been widely used to create strong anisotropic deformations in semimetals, is determined.

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## Hyperfine fields in $^{27}$Al nuclei in (Co$_{1-x}$Cu$_x$)$_2$MnAl alloys

### P.N. Stetsenko, V.V. Surikov, V.S. Pokatilov, A.I. Laskin, Yu.I. Avksentev

Moscow University Physics Bulletin 1986. 41. N 4. P. 131

The values of the lattice parameter, the mean magnetic moment, and the hyperfine field are experimentally determined in $^{27}$Al nuclei at T = 4.2 K in (Co$_{1-x}$Cu$_x$)$_2$MnAl alloys. A space overlap model is used in discussing the results.

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