Faculty of Physics
M.V. Lomonosov Moscow State University

# Issue 6, 1979

## Photoп spectrum equivaleпt of field of particle moviпg in external field

### Yu.G. Раvlеnkо

Moscow University Physics Bulletin 1979. 34. N 6. P. 1

An expression is obtained for the spectrum of photons equivalent to a particle moving in an external field; this is a generalization of the well-known result of Weizsacker and Williams.

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## То the question of nonstabllity of langmour vibrations of plasma iп the presence of relativistic beam with thermal dispersion of velocities

### L.S. Кuz'mеnkоv, Р.А. Роlуаkоv

Moscow University Physics Bulletin 1979. 34. N 6. P. 7

We investigate the influence of relativistic effects and radiative damping on beam instability. Expressions are obtained for the increment, the effective excitation width of the waves, and the criteria for the occurrence of instability, enabling one to draw a number of new physical conclusions. In particular, in a dense enough plasma the beam instability can be suppressed by radiative damping. We make numerical estimates. For large values of the plasma density and beam energy the effective excitation width of the waves can be so small that excitation of plasma waves becomes practically impossible.

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## Creation of electron-positron pairs Ьу а massive photon iп magпetic field

### V.Ch. Zhukоvskii, Shаrif АЬdаllа Наmid

Moscow University Physics Bulletin 1979. 34. N 6. P. 12

We examine the production of $e^{+}$ $e^{-}$ pairs by a massive photon and the annihilation of $e^{+}$ $e^{-}$ pairs with the formation of a massive photon in13 an ultrastrong magnetic field $H≥ B_{0}= 4.41∙10^{13}G$. We obtain the conditions under which the external magnetic field begins to exert a substantial effect on these processes.

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## Method of douЬle iпtegral transformations for Fredholm's equations of the first kind

### V.В. Gоstеv, А.R. Frеnkin

Moscow University Physics Bulletin 1979. 34. N 6. P. 18

We propose a method of solving (without investigating the questions of convergence and the possibility of readjusting the limits of integration) Fredholm (Volterra) integral equations of the first kind, which, if only formally, admit exact inversion. We describe a class of kernels to which one can apply the method of double integral transforms. Examples of exactly solved integral equations are given.

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## Оn the mutual synchronization of two spin generators

### Е.А. Кlivаdеnkо, М.S. Роlуаkоvа

Moscow University Physics Bulletin 1979. 34. N 6. P. 27

The problem of the stability of generation of a spin oscillator with an inhomogeneously broadened line of the working material is examined for the example of two spin oscillators coupled by a common transverse magnetic field. The single-frequency regimes are investigated in detail for equal and unequal transverse and longitudinal relaxation times and nonzero phase angle in the feedback circuit. Particular attention is paid to the study of the nature of the beats outside the region of stable single-frequency operation.

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## Method measurement of thermal diffusity of semitransparent materials of high temperatures

### R.Р. Yurсhаk, А.А. Меgаkhеd

Moscow University Physics Bulletin 1979. 34. N 6. P. 33

We propose a method of measuring the thermal diffusivity of partially transparent materials at high temperatures. The method is based on the application of the method of plane temperature waves for various thicknesses of the objects under study in the limit of an optically thin layer over a wide interval of heating frequencies. The method is tested by measuring the thermal diffusivity of high-quality fused quartz, which has an appreciable photon component of the heat transfer.

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## Operations of reciprocatioп апd inversion of complex physical values

### V.I. Shеstаkоv

Moscow University Physics Bulletin 1979. 34. N 6. P. 39

The operations of reciprocation $V^{-1}$ and inverse $V^'$ of indefinite complex physical quantities are defined and investigated. It is noted that the operations of additions, inverse (harmonic) addition $V_{1}∙V_{2} =(V_{1}^' + V_{2}^')^'$, and inversion of indefinite complex quantities $V_{1}$ and $V_{2}$ are generalizations of the basic operations of Boolean algebra. At the end of the article, we examine the question of whether the inversion operation can actually (physically) be carried out for any complex (and in particular, real) physical quantities.

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## On the role of vibrational excitations of а molecular system in the slow relaxation kinetic of charge on а semiconductor surfасе

### V.F. Кisеlеv, S.N. Коzlоv

Moscow University Physics Bulletin 1979. 34. N 6. P. 48

It is shown that the activation energy of the slow relaxation of charge in the field effect depends on the energy of the vibrational modes of absorbed molecules. The reason for the small capture cross sections of the slow electronic states is discussed. A capture model is proposed which explains the temperature dependence of the slow-relaxation kinetics in various gaseous units.

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## Temperature depeпdence of stationary radiolumiпescence in two levels system

### Т.S. Веssоnоvа, А.I. Sоbkо

Moscow University Physics Bulletin 1979. 34. N 6. P. 55

Starting from the well known equations describing the kinetics of variations in the concentrations of free and localized charges in a crystal, we give an interpretation of the dependence of the intensity of stationary radioluminescence (RL) on temperature and on the concentration of chromium impurities in heavily doped ruby. Calculations are carried out for a band model containing one electronic and one hole level for arbitrary occupation of the traps. According to the results obtained, the experimentally observed independence of the intensity of stationary RL on the activator concentration can be explained in terms of the above model if it is assumed that there is no recombination. It is found that after a sudden drop in the stationary RL intensity in the R lines as the temperature is lowered, the level of luminescence in heavily doped ruby should remain unchanged during irradiation. This conclusion is in complete agreement with the available experimental data.

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## The effect of moving irregularities on the motion of solid particles in a turbulent flow

### N.А. Мikhауlоvа, S.G. Веlоshарkоvа

Moscow University Physics Bulletin 1979. 34. N 6. P. 62

The statistical processing of a high-frequency motion picture has enabled us to establish that a flow interface consisting of individual discrete particles is a surface which varies in time and space with a deviation from its average position on both sides which is of the same order as the average height of the jumps of the solid particles. The take-off level of the solid particles in these jumps is with large probability higher than the landing level. The distribution of rms deviations of the vertical component of the velocity of the solid particles over the flow depth has two maxima (above the average interface and at the level of the interface). On the distribution curve for the rms deviations of the horizontal velocity component only the first maximum is clearly expressed.

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## Some of periodic perturbatioпs iп translatory-rotatory motioп of Мооп and Mercury

### Yu.V. Ваrkin

Moscow University Physics Bulletin 1979. 34. N 6. P. 67

The periodic solutions of Poincare to the problem of planar translational- rotational motion of a solid body in the attractive field of a sphere are used to elucidate the periodic perturbations in the motion of the Sun-Mercury and Earth-Moon systems. The necessary conditions for the stability of the periodic solutions are obtained and analyzed, and the theoretical values of the parameters $δ = (B - C)/B - A)$, where A, B, and С are the principal central moments of inertia of the body, are found in accordance with these conditions. For the Moon, $δ_{L}=1,5$ and for Mercury, $δ_{M}=1,18$. The periodic solutions give theoretical values of the librations of the Moon and Mercury in the orbital planes (26.175" for the Moon and 10.098" for Mercury). The periodic perturbations of the semimajor axis of the lunar orbit due to the asphericity of the Moon have an amplitude of 1.669 m. The angular distance to the perigee undergoes oscillations of amplitude 0.076". Thus, for determining relativistic effects in the motion of the Moon it is important to take rigorously into account the connection between the translational and rotational motions of the Moon. The perturbations of the orbital motion of Mercury due to its asphericity are of insignificant size.

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## Effect of deuteration on the spectra of spontaneous parametric light scattering in crystals of the $KH_{2x}D_{2(x-1)}PO_{4}$ system

### E.D. Mishina

Moscow University Physics Bulletin 1979. 34. N 6. P. 109

## Equations of motion for the densities of classical dynamical variables in external fields

### V.А. Кrаsnikоv

Moscow University Physics Bulletin 1979. 34. N 6. P. 77

We obtain in compact form the equations of motion for the densities of the classical dynamical variables in a wide class of external fields. We also examine the linear approximation in the gradients of the external fields.

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## Remark to the field theory with quantiгed space-time

### А.Е. Pukhоv

Moscow University Physics Bulletin 1979. 34. N 6. P. 81

We examine the theory of quantized space-time developed by V. G. Kadyshevskii and co-workers. In this theory momentum space is a surface of constant curvature: $(π^0)^2 — (π^1)^2 - (π^2)^2 — (π^3)^2 + (π^4)^2 = 1$. Each value of the physical four-momentum $p^μ= π^μ$(μ = 0, 1, 2, 3) corresponds to two points in momentum space π and $π^*$, which differ by the ii sign of $π^4$. Using the conditions of translational invariance and the microcausality of the S matrix, we show that the retarded functions for n ≥ 2 satisfy the relation $R_{n}(π_{0}{1},..., π_{n})= -R_{n}(π_{0}^{*},π_{1},...,π_{n})$ which connects the values of the matrix elements in the region $π^{4}>0$ with the values of the matrix elements in the region $π^{4}<0$.

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## Rays scattering iпdicatrix in flat-stratified medium with aпisometric irregularities

### S.М. Golynsky, N.Р. Ovchinnikova

Moscow University Physics Bulletin 1979. 34. N 6. P. 85

We present a theoretical analysis of how the parameters of the scattering indicatrix of rays on exit from an isotropic refracting medium with ellipsoidal inhomogeneities depend on the azimuth and length of the airways, the magnetic inclination at the point of reflection, and the geometry of the scattering inhomogeneities.

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## А laser Doppler velocimeter with an electrooptic modulator for the analysis of slow variaЬle sign flows with continuous velocity spectrum

### А.V. Рriеzzhеv, А.G. Тikhоmirоv, V.А. Jаkоvlеv

Moscow University Physics Bulletin 1979. 34. N 6. P. 89

We discuss the problem of employing an electro-optical shift of the frequency of laser radiation in laser Doppler velocimetry. We examine a differential laser Doppler velocimeter that was designed for studying slow variable-sign flows. We present the results of measurements of the flow of cytoplasm in living cells.

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## Losses measurement in quasioptical resonator with small unstability

### F.А. Коrоlеv, W.G. Воgоmоlоv, W.I. Кislоv

Moscow University Physics Bulletin 1979. 34. N 6. P. 93

We investigate experimentally the model Q-factor of an asymmetric unstable resonant cavity as a function of a parameter which is equivalent to the Presnel number for each mirror. Different values of this parameter can be obtained by varying the mirror separation, this is not the case in the method of diaphragming the beam at the exit mirror which has been applied in the past. Our results show that in certain limits one can obtain the required characteristics (size of losses and mode operation) of the resonance system by simply changing its length.

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## The theory of the stimulated sinchгotron radiation iп ultrarelativistic case

### F.А. Коrоlеv, А.V. Тuluроv

Moscow University Physics Bulletin 1979. 34. N 6. P. 97

We examine the possibility of stimulated synchrotron radiation being generated by an electron moving at a relativistic velocity along the magnetic field direction. The limiting condition for the highest harmonic that can be generated is obtained, and it is shown that stimulated synchrotron radiation is possible for high harmonics as well as low. The treatment is based on quantum theory.

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## АЬоut «suреrсоherеnt» states properties

### S.Р. Viаtсhаnin

Moscow University Physics Bulletin 1979. 34. N 6. P. 100

Sufficient conditions for a quantum oscillator to be located in a state with a phase uncertainty ∆φ≅1/n (n is the average number of photons) are formulated, and a method of measuring the phase of such states is proposed.

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## Electron-microscopic analysis of the dimensions of the mitochondria during the fluctuation of ionic beams

### Е.L. Кhоlmukhаmеdоv, G.В. Кhоmutоv

Moscow University Physics Bulletin 1979. 34. N 6. P. 104

We present a method of calculating the true size of mitochondria according to the area of the sections obtained in electron photomicrography and give the results of such a calculation for mitochondria in a fluctuating state. The results obtained for mitochondria in different phases of the fluctuational cycle shows that the mean radii of mitochondria in the shrunken and swollen states differ by a factor of 1.8.

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## Elliptical polarization of acoustic shear waves in a GDS crystal

### 0.S. Guba

Moscow University Physics Bulletin 1979. 34. N 6. P. 108

## Mathematical modeling of ecological systems having a cycle of biogenous elements

### V.E. Topnikov

Moscow University Physics Bulletin 1979. 34. N 6. P. 110