Faculty of Physics
M.V.Lomonosov Moscow State University

## Gauge invariant counterterms in electrodynamics

### S.V. Budnik and D.A. Slavnov

Moscow University Physics Bulletin 1979. 34. N 5. P. 1

A modification of the R-operation ($R ̂$-operation), which agrees with the gauge invariant Pauli-Willars regularization for electrodynamics is A constructed. The $R ̂$-operation is used to prove the gauge invariance of the S-matrix.

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## Dynamic deformability of the nucleus and its effect on the structure of photoabsorption and on the characteristics of photodisintegration

### F.A. Zhivopistsev and К.V. Shitikova

Moscow University Physics Bulletin 1979. 34. N 5. P. 7

The microscopic theory of specific highly excited states of the atomic nucleus - gigantic dipole resonances, is considered. Particular attention is given to the effect of different kinds of complex states on the structure of a gigantic resonance and on the photodisintegration characteristics. The process of linkages for the more complex states (both collective and noncollective in nature) leads to a condition, when a certain number of quasi-particles is added to a filled shell, sufficient for the spherical shape of the nucleus to become unstable (to a change in the properties of the surface etc.). In this case the closed shell is disturbed, which also causes an increase in the deformability of the composition of the nucleus in the highly excited state. The statistical group of states 2p2h, 3p3h etc. which ensures the statistical irreversible process of preequilibrium decay is of considerable importance in explaining the photodisintegration characteristics of atomic nuclei.

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## Multidimensional probability distributions of the envelope and phase of stationary noise with n0n6aussian statistics

### Yu.E. D'yakov

Moscow University Physics Bulletin 1979. 34. N 5. P. 14

It is shown that there is a unique relationship between the probability distributions of the envelope p(t), the phase ϕ(t), and a quasi-harmonic random process ξ(t) =p(t)cos ψ, $ψ = ω_{о}t+ ϕ(t)$ if ξ, p and ф are stationary. The structure of the distribution functions is obtained. The two-dimensional case is considered in detail. The results are generalized using a model of the quasi-periodic process ξ(t) =p(t)F(ψ), where F(ψ)= F(ψ+2n).

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## Discretization of radio signals in a parametric circuit with video pulse pumping

### V.P. Komolov and V.A. Roznyatovskii

Moscow University Physics Bulletin 1979. 34. N 5. P. 23

The results of an experimental investigation of the conversion of modulated radio signals in a parametric circuit with video-pulse pumping are presented. The possibility of using such a circuit as an effective high-speed device for gating modulated radio signals which enables the signal/noise ratio in synchronous reception to be improved is demonstrated.

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## Nonlinear amplification of sound in piezoelectrical semiconductors and self-synchronization of modes in acoustoelectric generators

### P.S. Landa

Moscow University Physics Bulletin 1979. 34. N 5. P. 29

The shape and amplitude of the oscillations of carrier density, of the electric field, and of elastic displacement in the saturation mode is calculated for nonlinear amplification of sound by crystals of piezoelectric semiconductor. The results obtained provide a qualitative picture of the self-synchronization mode of operation in acoustoelectric generators.

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## The theory of reflection from a mossbauer mirror. the anisotropic case

### M.A. Andreeva, S.F. Borisova and R.N. Kuz'min

Moscow University Physics Bulletin 1979. 34. N 5. P. 36

The theory of the mirror reflection of Mossbauer radiation for specimens containing Mossbauer nuclei when there is hyperfirie interaction, investigated in 1963 by Bernstein et al is investigated. On the basis of an invariant approach to the optics of anisotropic and gyrotropic media, developed by Fedorov, a general solution is obtained of the boundary value problem in the most general case when the reflecting medium is represented by permittivity and permeability tensors of arbitrary form. The reflection coefficient Is expressed in terms of the natural polarizations of the refracted wave. Detailed calculations of the natural polarizations and the reflection coefficient are made for the case when μ=1 and ε=1+ас с*, and also for ε=1, and μ= 1+ас с*. The need to separate the contributions of the electric and magnetic currents to the generalized permittivity function e when solving the boundary value problems is pointed out. Estimates are given for the difference in the correct expressions for the reflection coefficient from Fresnel's relations in the general case for weakly anisotropic media ($α~10^{4}$)and glancing angles of incidence ($θ~10^{-3}$), and it is found that these differences may reach 10%.

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## Superradiation under bragg diffraction conditions

### A.V. Andreev, R.V. Arutyunyan, and Yu.A. Il'inskii

Moscow University Physics Bulletin 1979. 34. N 5. P. 45

The kinetics of superfluorescence under anomalous gamma-quanta penetration conditions are considered. It is shown that when the Bragg condition is satisfied the superfluorescence mode is similar to the singlemode condition with certain characteristic values of the parameters. The direction of propagation of the Borrmann mode is a distinct direction in the crystal. The radiation pattern of the radiation will be determined by the intersection of the diffraction pattern of the working material and the Bragg diffraction cone. The use of high-multipole working transitions may reduce the generation threshold by an order of magnitude.

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## Effect of electron irradiation on the growth of films of certain metals (Al, Сu, Sb) on dielectric substrates

### E.M. Dubinina, S.S. Elovikov, A.S. Ovsyanitskii, G.P. Netishenskayas and E.P. Kirilenko

Moscow University Physics Bulletin 1979. 34. N 5. P. 52

The effect of electron irradiation on the growth of films of Al, Cu, and Sb on single-crystal specimens (NaCl) and on unoriented substrates of glassceramic and silicon monoxide (SiO) is investigated. It is shown that when layers of these metals are grown on crystals of NaCl electron bombardment usually leads to a reduction in the epitaxy temperature. Films deposited on amorphous specimens have greater degree of ordering when bombarded with electrons.

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## A form of the equations of the many-body problem

### L.G. Luk'yanov

Moscow University Physics Bulletin 1979. 34. N 5. P. 60

A transformation, which is a generalization of the Nekhyil transformation for the limited three-body problem is considered for the equations of the many-body problem in a moveable system of coordinates. The angle of natural rotation of the movable system of coordinates is taken as the independent variable, while the coordinates are subjected to a compression transformation. It is shown that the equations of motion after this transformation preserve the symmetry properties of the solutions, known for the initial equations.

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## The variational principle in the general theory of relativity

### V.N. Ponomarev and A.A. Tseitlin

Moscow University Physics Bulletin 1979. 34. N 5. P. 65

It is pointed out that the Hilbert Lagrangian in the general theory of relativity (the scalar of the curvature) is not characteristic for the boundary value problem for Einstein's equations in view of its linearity with respect to the leading derivative of the metric. This is due to the fact that for the boundary term in the variation of the action to vanish it is necessary to specify additional boundary conditions which contradict the order of Einstein's equations. This is illustrated with an example from mechanics. The characteristic Lagrangian for Einstein's equations is the "truncated" Dirac Lagrangian (following from the guage approach to the general theory of relativity), operation with which is similar to the addition to the Hilbert Lagrangian of a "boundary term" (as was assumed by Gibbons and Hawking). The need for this addition is pointed out.

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## Cherenkov radiation of monochromatic beams of particles taking their interaction into account

### I. V. Lupandin

Moscow University Physics Bulletin 1979. 34. N 5. P. 68

A formula Is derived for the intensity of the Cherenkov radiation of a beam of particles taking the dispersion of the velocities and of the initial coordinates and interference effects into account. The intensity of the radiation turns out to be dependent on the parameters characterizing the coordinate and velocity distribution of the particles of the beam, and also on the duration of the radiation. Models of the experiments to study the energy and spatial parameters of beams of particles are discussed.

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## Nonlinear high-frequency properties of disordered semiconductors

### I.P. Zvyagin

Moscow University Physics Bulletin 1979. 34. N 5. P. 72

A kinetic equation is obtained for the high-frequency components of the filling function of local states in disordered semiconductors. The equation obtained is used to estimate the nonlinear susceptibility due to migrations between localization centers randomly situated in space.

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## The hierarchical model of the universe and particles

### D.D. Ivanenko and V.G. Krechet

Moscow University Physics Bulletin 1979. 34. N 5. P. 76

A new static spherically symmetrical solution of the combined Einstein system of equations and the massive vector field is given taking the cosmological term into account. The solution can be regarded as an analog of the well-known Schwartzchild and Reissner-Nordstrom solutions for the case of a self- gravitating massive vector field. It is shown that the configuration considered forms a closed nonuniform cosmological model, whose mass and radius correspond in order of magnitude to the same parameters of the observed Universe. It turns out that when the length scale is changed, the cosmological model obtained has the parameters of an elementary particle.

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## Large distance cavendish experiments

### V.N. Rudenko

Moscow University Physics Bulletin 1979. 34. N 5. P. 80

The hypothesis of the variations of the gravitational constant when the distance between the attracting masses is increased is considered. It is shown that at the present time there are two possible ways of checking this hypothesis experimentally. The first consists in using sensitive modern gradiometers to measure G at distances ~ 10m with an accuracy of 1%. The second consists in using second-generation gravitational antennas, which should enable one to measure G at distances ~100 m with an accuracy of 0,1%. In the latter case the experiment is identical with the procedure for calibrating a gravitational antenna in components of the Riemann tensor. The results of these experiments enable one to formulate limitations on the mass of the particles of the hypothetical field responsible for the interaction, which differs from the Newtonian field.

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## A transducer for second-generation gravitational waves antennae

### V.B. Braginskii, Yu.B. Lanin and V.I. Panov

Moscow University Physics Bulletin 1979. 34. N 5. P. 85

The construction of a displacement transducer for a gravitational antenna based on a superconducting microwave resonator of special construction which enables the effect of low-frequency seismic interference to be reduced, is proposed. A theoretical and experimental investigation of this transducer is described.

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## Experimental investigation of the characteristics of the diffraction yield of an unstable quasi-optical resonator

### F.A. Korolev and V.G. Bogomolov

Moscow University Physics Bulletin 1979. 34. N 5. P. 89

The field distribution of the radiation at the output of a confocal unstable resonator at a wavelength of 7.2 mm is measured. The results are compared with theory for the far-field region. The results obtained confirm the correctness of the theoretical approach used and enable the degree of directivity of the output radiation to be estimated.

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## A diffraction-grating device for measuring the vibrations of diffusely reflecting objects

### V.S. Anchutkin

Moscow University Physics Bulletin 1979. 34. N 5. P. 92

A practical method of measuring small transverse vibrations of diffusely reflecting objects, the basic principle of which is the use of the oscillatory motion of a system of Interference fringes modulating the spectrum-structure of the scattered field, is described. The main element of the system is a diffraction grating with specularly reflecting rulings and transparent gaps between them, which serve simultaneously to illuminate the specimen and to spatially filter the scattered radiation.

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## The magnetic state of the V$^{3+}$ ions in ferrites with the spinel structure

### A.N. Goryaga and L.A. Skipetrova

Moscow University Physics Bulletin 1979. 34. N 5. P. 95

The magnetization Is and coercive force Hс of ferrites of the system $NiFe_{2-x}VxO_{4}$ where x = 0.00, 0.25, 0.50, 0.67, 0.80 and 1.00 are invesdtigated. The effective value of the magnetic anisotropy constants are found for all the specimens using the equation |K$_eff$| = 4ПIsHс at 80K. It is shown that the contribution of the $V^{3+}_B$ ions to the magnetic anisotropy is small and has a positive sign. It is suggested that in the crystal field of an octahedral complex the orbital triplet of the $V^{3+}$ ion is split in such a way that the orbital singlet becomes lower.

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## The behavior of the magnetostriction of copper ferrite at low temperatures

### L.P. Belov, A.N. Goryaga and L.G. Antoshina

Moscow University Physics Bulletin 1979. 34. N 5. P. 99

Были изучены температурные зависимости энергии активации, магнитострикции, магнетосопротивления и других магнитных свойств медного феррита в низких температурах. На основе полученных экспериментальных данных сделан вывод о том, что аномальное поведение магнитострикции медного феррита связано с возникновением в низких температурах прямого обменного взаимодействия.

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## The direction of rotation of spiral galaxies

### I.I. Pasha

Moscow University Physics Bulletin 1979. 34. N 5. P. 102

## The melting of heteropolymer chains when the cooperative energy depends on the type of boundary

### E.I. Shakhnovich

Moscow University Physics Bulletin 1979. 34. N 5. P. 104

## Prediction of the critical volume of liquids

### A.D. Okhotsimskii

Moscow University Physics Bulletin 1979. 34. N 5. P. 105