Faculty of Physics
M.V.Lomonosov Moscow State University

## Theory of multiple scattering in a semi infinite spatiallyinhomogeneous medium (II)

### Yu.B. Chernyak and G.G. Solov'ev

Moscow University Physics Bulletin 1977. 32. N 2. P. 1

Two simple models of the spatial dependence λ(z) are used with first- and secondorder perturbation theory (developed in [1]) to determine the intensity of the emerging radiation and the coefficient of reflection in the case of monochromatic scattering in a semiinfinite medium. Higher-order perturbation theory is briefly discussed. The results obtained can be used in model calculations to take into account the roughness of the surface of a light-scattering medium, and to determine the light-scattering characteristics of diffusely reflecting dyes as functions of surface properties.

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## A universal method for the symbolic representation of cascade connected two-port networks

### V.I. Shestakov

Moscow University Physics Bulletin 1977. 32. N 2. P. 9

Standard matrix methods were shown in [1] to be unsuitable for the symbolic representation of cascade connected two-port networks (quadrupoles) when at least one of the branches has an infinite impedance. In this paper, we give a further development of the previously proposed representation of cascade connected twoport networks, and show that the method is valid for any values of the branch impedances, both finite and infinite.

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## Spectroscopic determination of the temperature and concentration of strontium atoms and ions in a discharge produced гм a cooled hollow cathode

### L.M. Volkova, A.M. Devyatov, and V.Kh. Fazlaev

Moscow University Physics Bulletin 1977. 32. N 2. P. 17

Spectroscopic data on the discharge initiated in a cooled hollow cathode are used to determine the discharge temperature and the concentration of atoms and ions of strontium.

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## New solutions of the solidification and melting problems

### A.A. Pomerantsev

Moscow University Physics Bulletin 1977. 32. N 2. P. 21

A method is developed for the solution of the one-dimensional problem of thermal conduction with the moving boundary conditions, namely, the problem of solidification and melting. By transforming the variables, the problem Is reduced to that of fixed boundary conditions. Examples of solutions are reproduced

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## Evaluation of the collision integral and solution of the basic equations of electromagnetic cascade theory

### A.A. Belyaev, I.P. Ivanenko, and A.A. Kirillov

Moscow University Physics Bulletin 1977. 32. N 2. P. 26

A new analytic solution is presented for the one-dimensional problem of electromagnetic cascade theory, taking into account ionization losses and the Landau- Pomeranchuk effect. The ionization losses are not assumed to be proportional to the variation in the number of particles in the shower, but are taken into account by direct approximation of the collision integral, so that the specific properties of the medium are more accurately taken into account. The proposed approximation and the solution presented in this paper can be used to obtain the distribution functions with their prescribed accuracy. These solutions are valid in a broad energy range and yield improved versions of known distribution functions.

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## Differential equations for the nonangular elements of a hyperbolic orbit

### V.M. Chepurova

Moscow University Physics Bulletin 1977. 32. N 2. P. 30

Differential equations are presented for the nonangular elements (semimajor axis, eccentricity, and inclination) of an intermediate hyperbolic orbit of a mass point moving in the gravitational field of a condensed planet, subject to a perturbation by another planet. The intermediate orbit is based on the symmetric variant of the problem of two fixed centers. The perturbation function is taken in the form of the Hill term in the expansion of the potential due to the perturbing planet, corrected for the elliptical character of its motion. The righthand sides of the equations are in the form of trigonometric series whose arguments are combinations of the angular elements of the intermediate motion of the mass point and the angular elements of the perturbing body, whereas the amplitudes depend on the nonangular elements of the two and are series In powers of the small parameter of the problem of two fixed centers.

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## Field distribution and spatial coherence of amplified spontaneous emission at $3.39_μ$ in a helium-neon laser

### F.A. Korolev, A.I. Odintsov, and Khaled Susu

Moscow University Physics Bulletin 1977. 32. N 2. P. 38

An experimental study has been carried out of the field distribution over the cross section of the 3.39 μ ASE beam from a helium-neon laser with a discharge tube 4 m long and 10 mm in diameter, operated far from saturation. It was found that the beam is channeled in the active medium of the laser and the result of this is that the beam diameter becomes much smaller than the tube diameter and, at the same time, the angular divergence of the beam approaches the diffraction limit.

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## Dynamic damping during measurements of small forces

### N.V. Gordienko, A.V. Gusev, and V.N. Rudenko

Moscow University Physics Bulletin 1977. 32. N 2. P. 42

Measurements of small forces by radiophysical methods based on the response of a mechanical oscillator are discussed. It is shown that a quasi-ideal transducer can be developed by using the dynamic damping of the transducer noise at a partial oscillator frequency. A calculation is given for an oscillator with a parametric capacitive transducer.

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## A fast pulsed bridge-connected measuring converter

### N.N. Dmitrieva

Moscow University Physics Bulletin 1977. 32. N 2. P. 47

A description is given of a new pulsed resistance-period converter of high sensitivity. It is designed for operation with bridge-converted variable-resistance probes. The period is varied by varying a capacitor and the characteristic of the converter is linear. When the probe resistance changes by 0.2%, the period changes by a factor of three. The converter is based on integrated circuits.

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## Spin effects using the motion of electrons in undulator tubes

### Yu.G. Pavlenko and A.Kh. Mussa

Moscow University Physics Bulletin 1977. 32. N 2. P. 50

An analysis is given of the influence of quantum-mechanical properties of radiation on the spin states of particles moving in an arbitrary undulator tube. The resulting expression for the spin-flip transition probability as a function of the particle energy and the anomalous magnetic moment is examined.

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## Parametric interaction of electromagnetic oscillations in nonlinear dielectric resonators: basic equations

### G.V. Belokopytov

Moscow University Physics Bulletin 1977. 32. N 2. P. 54

The method of slowly-varying standing waves is used to obtain the truncated equations for the three-frequency resonance parametric interaction in nonlinear dielectric resonators. The equations are suitable for inhomogeneous and anisotropic media. Pump reaction and nonlinear detuning of both electrical and thermal character are taken into account.

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## Active compensation of noise in the michelson interferometer

### M.A. Vorontsov and V.I. Shmal'gauzen

Moscow University Physics Bulletin 1977. 32. N 2. P. 60

A general approach is developed to noise compensation in the Michelson Interferometer. Compensating systems containing sensitive elements with distributed parameters are examined. A highly stable practical system is proposed.

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