Faculty of Physics
M.V.Lomonosov Moscow State University

Dependence of potential on characteristics of discrete spectrum in quantum mechanics

V.B. Gostev, A.R. Frenkin

Moscow University Physics Bulletin 1983. 38. N 5. P. 1

Using a general solution of the inverse problem for tbe reconstruction of a confining potential $(\tilde{V}(r) \to \infty, r \to \infty$) from a reference potential $V(r)$, energy levels and normalizing constants, we analyze the corrections to the potential $\Delta V(r)$ and to the regular solutions of the radial Schrodinger equation when a finite number of the spectral characteristics are changed. For $r \to 0$ and any arbitrary changes of the spectrum $\Delta V(r) \sim r^{2l+1}$ ($l$ is the orbital angular momentum). For $r \to \infty$, the asymptotics of $\Delta V(r)$ are classified according to three different types of change of the spectral characteristics. It is shown that when additional energy levels are included or some energy levels are omitted, there is a one-to-one relationship between the asymptotic behavior of $\Delta V(r)$ and the period of radial oscillations of the classical motion in the field $V(r)$. All results can be carried through to the case of long-range attractive potentials ($\lim_{r\to\infty} = 0$, $\lim_{r\to\infty} r^2V(r = \infty)$, when the spectral density of the continuous spectrum is conserved.

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Magnetoresistance, Hall effect and magnetization of gadolinium monocrystals at helium temperatures and fields up to 63 kOe

L.V. Lazareva, O.S. Galkina

Moscow University Physics Bulletin 1983. 38. N 5. P. 7

We study the transverse magnetoresistance, the Hall effect, and magnetization of monocrystalline gadolinium with $m=\rho_{300K}/\rho_{4.2K}=41$ at temperature 4.2 K and fields $H_{e_{max}}$ = 63 kOe. In the true fields $H_i = H_e - 4\pi IN \gg H_{is}$, where $I$ is the magnetization, $N$ is the demagnetiization factor of the samples, and $H_{is}$ is the true saturation field, we observe an increase of magnetoresistance and a linear dependence of the Hall emf on the field, which are associated with the fulfillment of the strong-field criterion $h \omega_H \gg kT$, where $\omega_H$ is the cyclotron frequency. Using the measured Hall emf in the fields $H_i \gg H_{is}$, we estimate the normal Hall coefficients $R_0$ and the difference of the carrier concentration $\Delta N$ per atom of gadolinium.

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Application of double frequency spin generation for the measurement of frequency of light

S.D. Varlamov, Yu.S. Konstantinov, A.M. Smirnov

Moscow University Physics Bulletin 1983. 38. N 5. P. 13

The spin generation at two lines of NMR sample makes it possible to measure accurately the spectral interval between these lines. If the measured spectral interval is temperature dependent, the heating of the sample can be determined from the change of the spectral interval. When the sample is illwninated by light, the rate of heating of the sample is related to the light intensity. It is suggested that the double-frequency spin generation can be used to measure the light intensity absorved by a sample in the sensor of NMR spectrometer.

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Estimate of the parameters of external perturbation of a test oscillator with RC sensor

S.I. Babichenko, V.N. Rudenko, A.G. Yagola

Moscow University Physics Bulletin 1983. 38. N 5. P. 17

Using numerical modeling, we estimate the parameters of an external force of a given form which perturbs a test oscillator with a registering relaxation circuit. The method and results are presented for two typical pulse signals with allowance for readout errors and the fluctuation of parameters of the registering circuit.

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Measuring-computational complex. Problems of reduction of the results of measurements

Yu.P. Pyt'ev

Moscow University Physics Bulletin 1983. 38. N 5. P. 23

We consider the reduction problems for a measuring computational complex "device+ computer", which make it possible to improve considerably the characteristics of experimental instruments. It is shown how the investigator can use the complex as a device with given parameters.

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Choice of intermediate orbits for the outer satellites of Jupiter

A.A. Orlov, N.A. Solovaya

Moscow University Physics Bulletin 1983. 38. N 5. P. 28

It is suggested, using results of a numerical investigation, that various variants of the intermediate orbits may be useful for the construct ion of an analytical theory for the motion of the outer satellites of Jupiter.

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Numerical modeling of wave and oscillatory processes in active resonance transmission lines

E.V. Galuzo, V.I. Kanavets

Moscow University Physics Bulletin 1983. 38. N 5. P. 33

We model numerically the processes in a one-dimensional model of an active nonlinear resonant medium. Allowance is made for a close coupling between the wave and oscillatory phenomena, variable structure of the fields, and a variable spectrum. The model represents a discrete transmission line with resonance circuits which contain nonlinear components. We solve the nonstationary equations of the system, and the voltage distribution is found by the driving method. We study a number of nonlinear processes, including the radiation of the active layer and a mutual synchronization of the autogenerators with a narrowing of the spectrum.

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"Carcass" wavefunctions in many-particle variational calculations

P.P. Zakharov, N.N. Kolesnikov, V.I. Tarasov

Moscow University Physics Bulletin 1983. 38. N 5. P. 41

We present a refined procedure for many-particle variational calculations. The procedure is based on the use of "carcass" trial wave-functions which reach a maximum for a definite spatial configuration of the particles. This configuration is given by a system of variational vectors. Using the example of three- and four-particle calculations we show that this procedure is capable of improving considerably the convergence of the variational calculations. Despite the more complex form of the matrix elements this procedure is, in many cases, more economical than the analogous calculations with non-carcass wavefunctions.

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Calculation of the single and double ionization cross sections of helium by protons

V.A. Disorovich, V.S. Nikolaev

Moscow University Physics Bulletin 1983. 38. N 5. P. 46

The independent-electron approximation is used to calculate the single and double ionization cross sections of helium atoms by protons with energies $E$ from 0.01 to 5 MeV. The calculation is carried out for three variants of the one-electron transition probabilities to the continuum. For all energies $E$, the results of the calculation agree qualitatively with experiment, and for $E>$0.1 MeV, the calculated single ionization cross sections coincide with the experimental values. The double ionization cross sections for $E=$0.2-0.7 MeV lie higher, and for $E=$1.5-4 MeV, than the experimental values. This is apparently caused by the neglect of the shock effect on the ionization amplitude.

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Absorption in systems of multilayer interference light filters. Effective systems of light filters

A.Yu. Klement'eva, L.S. Kornienko, A.V. Grishkin

Moscow University Physics Bulletin 1983. 38. N 5. P. 51

We study the spectral characteristics $T(\lambda)$, $A(\lambda)$, and $R(\lambda)$ of different types of multilayer interference light filters. It is shown that, at the expense of a higher complexity of light-filter system, one can obtain large values of the transmission coefficient $T_{max}$ for a given bandwidth and given physical parameters of the layers.

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Distribution of time resources for the measurements in an experiment

Yu.P. Pyut'ev, P.V. Golubtsov

Moscow University Physics Bulletin 1983. 38. N 5. P. 57

In experimental investigations, one often encounters a situation where a cycle of measurements id designed under the condition that the total duration of the measurements is fixed. In this work, we develop methods which make it possible, in a number of cases, to increase considerably the accuracy of the measurements. We introduce the notion of design efficiency, which makes it possible to estimate, without finding the optimal strategy, the decrease of errors as a result of the redistribution of the time resources between measurements.

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Theory of nonlinear optical picosecond spectrochronograph

I.Yu. Pirogova, A.P. Sukhorukov

Moscow University Physics Bulletin 1983. 38. N 5. P. 63

We consider the combined-frequency generation during the noncollinear interaction of very short light pulses in a nonlinear crystal. It is shown that it is possible to obtain information about the duration and spectrum of the optical pulse by measuring the space-angular radiation pattern of the combined frequency in two mutually perpendicular transverse direction. We present results of calculation of the dispersion of direction of the doubling synchronism for the crystals LiIO$_3$, KDP, and ADP.

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Theory of scattering of two quantum particles from a third heavy particle

A.M. Popova, Yu.Y. Popov

Moscow University Physics Bulletin 1983. 38. N 5. P. 69

We study the solution of Faddeev equation for the three-body problem in the limit when mass of one of the particles tends to infinity. It is shown that the solution does not have a continuous transition in this limit, and the required scattering amplitude for the two light particles from an infinitely heavy particle must be obtained by reconstructing the Faddeev equations, which reduces them to the equations of a two-body problem in a field.

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Excitation of autoionization states of atoms by electron impact using the Born and distorted-waves approximation

A.N. Grum-Grzhimailo, A.I. Magunov

Moscow University Physics Bulletin 1983. 38. N 5. P. 75

Using the Born and distorted-waves approximations, we develop a method for the description of inelastic scattering of intermediate-energy electrons from atoms, with allowance for the excitation of autoionization states. The excitation of the state $^4d-^1 5p^1 P$ of a cadmium atom is used to discuss some features of the resonant ionization which are due to the distortions of the incident and scattered waves in comparison with the plane-wave Born approximation.

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Amplitude dependence of internal friction in cesium iodide crystals

G.Z. Kurbanov, E.K. Naimi, N.A. Tyapunina

Moscow University Physics Bulletin 1983. 38. N 5. P. 81

We study the dependence of internal friction on the amplitude of ultrasound oscillation in the monocrystals of cesium iodide, which were plastically deformed during preparation and mounting; we also studied aged sample. In samples oriented along [110], we observe an amplitude dependence of the internal friction. It is shown that the internal friction is caused by the dislocation mechanism of ultrasound absorption. We estimate the change of the effective length of dislocation loops during aging.

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Recoil effects and quantum corrections in the semiclassical theory of synchrotron radiation

I.M. Ternov, V.A. Bordovitsyn

Moscow University Physics Bulletin 1983. 38. N 5. P. 85

In a linear approximation with respect to the spin and quadrativ with respect to the recoil parameter, we obtain quantum corrections to the power of synchrotron radiation of an electron. The spin correction is equal to $\xi \zeta$, and the first and second (boson) corrections are $(55\sqrt{3/24})\xi$ and $(56/3)\xi ^2$.

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Topological invariants in the generalized theories of gravitation

V.V. Trefilov, N.F. Nelipa

Moscow University Physics Bulletin 1983. 38. N 5. P. 88

For spaces with affine connectivity, we obtain a criterion for the existence of a generalized Euler's class and the Lanczos-Bach formula. It is shown that this criterion is fulfilled in the spaces of Weyl and Einstein-Cartan.

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Faster-than-light waves in relativistic plasma in a weak magnetic field

L.S. Kuz'menkov, M.I. Sitnov

Moscow University Physics Bulletin 1983. 38. N 5. P. 92

Using the kinetic theory, we consider the change of spectral properties of relativistic plasma when a weak external magnetic field is switched on. In the first approximation with respect to the field, faster-than-light cyclotron waves are absent. The longitudinal wave is transformed into the extraordinary wave in the region of small wave vectors, whose dimension is proportional to the square root of the cyclotron frequency. The dispersion of the ordinary wave in relativistic plasma at finite temperature in a weak field does not differ from the dispersion of the transverse wave in an unmagnetized plasma. The dispersion of the extraordinary wave is determined from a quadratic equation with respect to the square of the frequency of the wave.

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Light-beam propagation in optically inhomogeneous medium with anisotropic scattering

V.B. Eflov, Yu.A. Il'inskii

Moscow University Physics Bulletin 1983. 38. N 5. P. 96

It is shown that the transport equation in an optically inhomogeneous medium can be solved for narrow beam, assuming that the gradient of the refractive index is small. The result can be used for the calculation of the power of radiation incident on a directed receiver after diffuse reflection of the signal from a surface in an optically inhomogeneous medium.

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Magnetic phases and phase transitions in a {11l} film monocrystal

L.I. Antonov, L.E. Korotenko, A.N. Mateev, V.V. Popov

Moscow University Physics Bulletin 1983. 38. N 5. P. 99

For monocrystalline magnetic films of the type {11l} with cubic and single-axis anisotropies, we study the spectrum of homogeneous states for a given anisotropy parameter $S$, where $S=k_{\perp}-2\pi M^2/k_1$, $k_{\perp}$ and $k_1$, are the first constants of single-axis and cubic anisotropy, respectviely. It is shown that when the anisotropy parameters S changes, orientational phase transitions take place, and the majority of the orientational phase transitions takes place in the region of the values $\left | S \right | < 1$. This region of $S$ is characterized by a considerable increase of the number of magnetic phases. For the majority of cases, the solution is carried out numerically.

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Two-photon excitation of exciton-polariton quasi-solutions

V.D. Gora, V.I. Pustovoi, A.P. Sukhorukov, A.K. Sukhorukova

Moscow University Physics Bulletin 1983. 38. N 5. P. 103

We develop a theory of the generation of exciton-polaritons near the resonance by picosecond and subpicosecond pumping pulses. We analyze analytically and numerically the formation of stationary pumping pulses and excitons in conditions when the field intensity of the direct radiation on the boundary is high.

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Method of high-pressure measurements of the Mossbauer effect on the nuclei of tellurium 125

A.A. Kornilova, A.A. Opalenko

Moscow University Physics Bulletin 1983. 38. N 5. P. 107

We develop a method for a Mossbauer study at high pressures using radioactive samples, with extraction of radiation via a Bridgman anbil, made from boron nitride. The pressure calibration is carried out by measuring the lattice parameter of NaCl. We obtain Mossbauer spectra of tellurium and tellurium clioxide at pressures up to 110 kbar. In tellurium, we observe a decrease of the quadrupole splitting of the spectrum at pressures above 40 kbar, which corresponds to the points of first-order phase transition.

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Determination of average electron energy from the volt-ampere characteristic of the Langmuir probe

V.A. Dovzhenko, A.P. Ershov, A.A. Kuzovnikov

Moscow University Physics Bulletin 1983. 38. N 5. P. 111

It is shown theoretically that the volt-ampere characteristic of a Langmuir probe can be used to determine the average electron energy $<\epsilon>$ in very wide limits of variation of the electron energy distribution function. The required segment of the volt-ampere characteristic lies within the limits $\left(0, \frac{1}{3}<\epsilon>\right)$, and the maximum error in the determination of $<\epsilon>$, due to the deviation of the electron energy distribution function from Maxwellian, does not exceed 50%.

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