Faculty of Physics
M.V.Lomonosov Moscow State University

## Photoproduction of neutrinos on electrons in the two-dimensional qed approximation

### Yu.М. Loskutov, V.V. Skobelev

Moscow University Physics Bulletin 1980. 35. N 6. P. 1

Typical reactions of electronic- and muonic - neutrino production on the electron in a strong magnetic field are discussed in a Weinberg model. The resulting ratio of the corresponding cross sections, which depends on the mass of the charged boson, is, in principle, encouraging as to the possibility of estimating its mass from neutron - star neutrinoluminosity experiments.

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## Balance equation for nonequilibrium electrons distribution in the mobility gap of disordered semiconductor in presence of light

### V.B. Sulimоv

Moscow University Physics Bulletin 1980. 35. N 6. P. 7

A balance equation is derived for determination of the average occupation number of a certain state in the forbidden band when a disordered semiconductor is illuminated by monochromatic light. The method of none quilibrium temporal Green's functions is used for the calculation. Expressions are found for the nonequilibrium single-particle functions. Perturbation theory is used to take the effects of the light into account. The conditions to be imposed on the parameters of the problem for validity of the balance equation are stated. Among other things, it is shown that the mass - operator component that fluctuates with the period of the light can be neglected if the electron - phonon interaction constant is sufficiently small.

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## On the Green's functions of classical dynamical systems

### N.V. Peskov

Moscow University Physics Bulletin 1980. 35. N 6. P. 16

An algorithm for approximate calculation of the Green's function for nonlinear infinite - dimensional dynamic systems on the basis of series expansion of the canonical transformation that converts the nonlinear system to a linear one is described. A nonlinear wave equation with a cubic term is considered as an example.

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## A continuous laser with a lightguide resonator

### A.M. Zabelin, S.K. Isaev, L.S. Kornienko, V.V. Firsov

Moscow University Physics Bulletin 1980. 35. N 6. P. 22

The development and testing of a continuous garnet laser with a length of multimode quartz lightguide in its resonator is reported. Optimum conditions for excitation of various transverse modes in a laser with a lightguide resonator are calculated. It is established that strong transverse - index mode selection occurs in the lightguide resonator. It is shown experimentally that small changes in the configuration of the resonator can be made to tune the laser from one transverse mode to another. A single-mode regime corresponding to the selected lightguide mode is then excited in the multimode fiber. The calculated and experimental results indicate that incorporation of a lightguide into a laser resonator is an effective way to excite a single lightguide mode in a multimode fiber.

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## The fast Fourier transformation in the problem of thermal self-action

### S.S. Chesnokov

Moscow University Physics Bulletin 1980. 35. N 6. P. 27

The use of a spectral method based on the fast Fourier transformation to investigate the thermal defocusing of light beams in moving media Is described. The effectiveness of the approach in problems of the diffraction and self-action of beams with complex initial intensity distributions is discussed. An example is considered.

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## Coherent properties of X-Ray sources and coherence effects in X-Ray optics. I. Spatial coherence of synchrotrone radiation

### S.A. Akhmanov, B.A. Grishanin, G.A. Lyakhov, Yu.V. Ponomarуоv

Moscow University Physics Bulletin 1980. 35. N 6. P. 32

The correlation properties of syncrotron radiation are analyzed in the classical approximation with allowance for the random radial structure of the electron bunch and its relativistic and extended nature. It Is. shown that the classical treatment has limited validity for description of the coherence of hard X-radiation from a synchrotron source. The energy parameters of dynamic scattering (DS) of partially coherent Xray beams In perfect crystals are calculated. The effects of Imperfect coherence on extinction beats and the anomalous passage of waves under DS conditions are analyzed. The increase in the radius of coherent radiation due to the interference nature of DS is calculated. A method for measuring the coherence radius in the X-ray band with use of DS effects is discussed.

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## Coherent properties of X-Ray sources and coherence effects in X-Ray optics. II. Dynamical scattering of partially coherent X-Ray emission by crystals

### S.A. Akhmanov, B.A. Crishanin, G.A. Lyakhov, Yu.V. Роnomаrуоv

Moscow University Physics Bulletin 1980. 35. N 6. P. 39

The theory of dynamic scattering in perfect crystals is generalized to the scattering of partially coherent X - radiation. It is shown that, both the temporal and spatial incoherences have a strong influence on the course of the p rincipal effects: extinction beats are moved and anomalous transmission (the Borrman effect) deteriorates. The method of slow amplitudes is used to obtain general results that describe the transformation of the correlation functions of a scattered X-ray beam. It is shown that the coherence radius increases on dynamic scattering (in the X-ray analog of the van Zittert-Zernicke theorem). It is found that the extinction-beat smoothing effect can be used as a basis for measurement of the correlation functions; opportunities for obtaining information on the spatial and temporal correlation functions separately are examined.

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## On antenna arrays signals resolution

### V.A. Вurоv, О.V. Dmitriev

Moscow University Physics Bulletin 1980. 35. N 6. P. 52

Three basic problems that arise in signal resolution are examined: what i is the shortest angular distance between signal sources that can be resolved by a discrete array; what is the largest number of resolvable signal sources of unknown power, and what is the nature of optimum processing to resolve signal sources of unknown power that are close to one another? The results cited indicate that the resolution of an antenna array can exceed the Rayleigh limit and Is determined by the output signal/noise ratio, while the number of signals that can be resolved depends on the number of different spatial frequencies in the aperture; of the array. It is shown that in the Gaussian approximation, the optimum - processing algorithm for resolution reduces to weighted processing of estimates of the cross-correlation moments for signals from all elements of the array and makes it possible to ensure resolution near i the potential limit.

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## Systems of multilayer interference filters at oblique incidence of light

### F.A. Korolev, A.Yu. Klementjeva

Moscow University Physics Bulletin 1980. 35. N 6. P. 59

The angular properties of narrow - band and band optical filters of various types for the visible, UV, and IR regions of the spectrum are investigated. The basic behavior of the properties at angles from 0 to 60° are indicated with the aid of simple relationships and a matrix procedure. Types of systems with inclination - stable transmission-band contours and minimal variation of the characteristics with angle are designated as effectively performing angled multilayer systems.

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## About the boundary layers, formed on the density jumps

### E.P. Anisimova, L.V. Poborchaya, A.A. Speranskaya

Moscow University Physics Bulletin 1980. 35. N 6. P. 67

The results of an observational study of the structure of boundary layers formed on a density discontinuity are discussed, and the velocity profile in the mixing zone at the density discontinuity is calculated. It is shown that the velocity profile in a mixing layer on a density discontinuity can be calculated with Prandtl's formula for the boundary of a free jet if the variation of average velocity with the local Richardson number is taken into account.

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## To the method of study of magnetic transformations in amorphous and mictomagnetic materials

### K.P. Belov, A.N. Goryaga, A.I. Kokorev

Moscow University Physics Bulletin 1980. 35. N 6. P. 72

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## Nonlinear damping of waves in low-turbulent relativistic plasma

### L.S. Kuz'menkov, P.A. Polyakov, О.O. Trubachev

Moscow University Physics Bulletin 1980. 35. N 6. P. 104

A formula is derived for the nonlinear - damping decrement of Langmuir waves in a weakly turbulent relativistic plasma, and the limit of validity of the corresponding nonrelativistic expression is indicated. The nonrelativistic formula for nonlinear damping applies even at temperatures an order of magnitude lower than the electron rest energy.

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## Sound focusing by liquid sphere

### N.N. Makarсhenkо, F.V. Rоzhin, O.S. Tonakanov

Moscow University Physics Bulletin 1980. 35. N 6. P. 107

The conditions of focusing of sound by a liquid sphere in water are investigated theoretically, and various patterns observed on variation of the acoustic parameters of the liquid sphere are reported. The angular and radial variations of the acoustic pressure field are investigated at various temperatures. The problem is considered without attention to losses.

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## The fine structure of spectra of the recombination emission

### V.A. Mashtakowa, В.B. Shishkin

Moscow University Physics Bulletin 1980. 35. N 6. P. 111

An energy sufficient to form elementary excitations to levels exceeding the vacuum level of the electron fluid is released on recombination of thermal defects in transition metals. The recombination emission that results from this process is responsible for the experimentally observed fine structure of the volt - ampere characteristics of vacuum diodes with single - crystaltungsten and molybdenum electrodes. Medium - waveelectro - magnetic oscillationsoccur in the diode at zero bias.

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