Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## Renormalization of the Casimir energy with logarithmic divergences

### I.Yu. Malakhov, K.A. Sveshnikov, P.K. Silaev

Moscow University Physics Bulletin 2005. 60. N 6. P. 1

A procedure for the renormalization of the vacuum field energy in the case where the energy levels are known only numerically is proposed. It requires neither an explicit transcendental equation for determining the levels nor an analytical expression for the asymptotic behavior of these levels. The procedure yields an unambiguous result even when there is a logarithmic divergence in the expression for the vacuum energy.

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## Gravitational lensing on a brane

### Yu.V. Grats, V.V. Dmitriev

Moscow University Physics Bulletin 2005. 60. N 6. P. 7

An expression for the angle of light deflection in the gravitational field of a global monopole embedded in the Randall-Sundrum universe has been obtained. It has been demonstrated that the deflection angle depends on the characteristic parameter $k$ of the model, and thus, limitations for this parameter may in principle be obtained from astronomical observations.

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## Allowing for spin-current interaction by Breit's Hamiltonian in the hydrodynamic method

Moscow University Physics Bulletin 2005. 60. N 6. P. 12

Balance equations of momentum and magnetic moment density that allow for spin—current interaction are derived for a system of quantum particles.

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## Diagnostics of hidden damage in biological membrane under exposure to low-dose γ-radiation

### E.K. Kozlova, A.P. Chernyaev, P.Yu. Alekseeva, A.M. Chernysh, A.A. Dolgopolova, M.A. Nazarova

Moscow University Physics Bulletin 2005. 60. N 6. P. 18

Experimental data on the effect of low doses of gamma radiation on the membrane of human erythrocytes are presented. Hidden damage of erythrocyte membrane after exposure to $^{226}$Ra has been detected by applying a calibrated electric pulse. This method is compared with the classical method for assessing the state of a membrane by measuring osmotic fragility. A mathematical model for adequate description of experimental results is proposed.

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Atomic and nuclear physics

## Analysis of the anomalous behavior of $D^*$-meson production cross sections in deep inelastic $e^-p$ and $e^+p$ scattering in the hera collider

### R.K. Dement'ev

Moscow University Physics Bulletin 2005. 60. N 6. P. 22

An explanation is offered of the anomalous difference in the $D^*\!$-meson production cross sections discovered in the ZEUS experiment in deep inelastic $e^-p$ and $e^+p$ scattering in the HERA Collider.

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## Effect of electron shell nonsphericity of an excited ion on its stopping in electron gas

### L.L. Balashova, A.A. Sokolik

Moscow University Physics Bulletin 2005. 60. N 6. P. 31

The effect of nonsphericity of electron shells of ions, arising in their excitation in the course of passage through matter, on their stopping parameters is considered. The quantitative calculations are carried out within the framework of the dielectric theory for the stopping effective charge of fast nonrelativistic Li"'" ions in their passage through a carbon target. A substantial difference in stopping effective charges between ions with uniform, elongated, and compressed (relative to the direction of motion) electron shell distributions is established.

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## Using multidimensional pattern recognition techniques in classifying primary cosmic-ray particles

### E.B. Postnikov

Moscow University Physics Bulletin 2005. 60. N 6. P. 37

The application of statistical multidimensional pattern recognition theory to solving problems associated with the classification of primary cosmic-ray particles is studied. As an illustration, a practical problem that has not even an approximate solution within the deterministic approach is solved on the basis of model data. An algorithm that is used to divide the primary particles into two classes and employs the concept of a Bayes linear classifier is described, and a broad spectrum of problems of experimental space physics is specified whose solution can be achieved by using the proposed method.

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Optics and spectroscopy

## Improvement of a model of the fiber-optic parametric amplifier

### N.A. Poliektova$^1$, О.E. Nanii$^1$, M.A. Solodyankin$^2$

Moscow University Physics Bulletin 2005. 60. N 6. P. 43

A method to take account for dispersion variations over the length of real fiber light guides in a model fiber-optic parametric amplifier is suggested. The theoretical and experimental amplification spectra of the parametric amplifier in a high nonlinearity fiber under continuous pumping conditions are compared.

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## Possibility of laser asymmetric synthesis of hydrogen peroxide molecule enantiomers from a racemic mixture without preliminary molecular orientation

### Yu.V. Vladimirova$^1$, B.A. Grishanin$^1$, D.V Zhdanov$^1$, V.N. Zadkov$^1$, H. Takahashi$^2$

Moscow University Physics Bulletin 2005. 60. N 6. P. 47

Using hydrogen peroxide as an example, the specific features of the laser control of the chiral state of an initially racemic mixture of molecules without their preliminary orientation have been studied. The determining role of molecular rotations and the molecular ensemble temperature have been revealed, and promising schemes for the laser asymmetric synthesis of enantiomers from a racemic mixture have been proposed.

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Solid state physics

## Optimal size of hydrophobic associates in aqeous solutions of hydrophobic ally modified polyacrylamide

### Yu.A. Shashkina, V.A. Smirnov, О.E. Filippova

Moscow University Physics Bulletin 2005. 60. N 6. P. 53

Hydrophobic association of hydrophobically modified polyacrylamide in aqueous solutions was studied by fluorescence spectroscopy using pyrene as a probe. It is shown that an increase in the amount of associating n-nonylacrylamide units in a polymer leads to the increase in the amount of hydrophobic associates, with the average size of one associate remaining unchanged. Similar regularities are observed in a salt medium as well (in the presence of sodium chloride), however, in this case the average size of associates is much larger.

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## New method for determining parameters of potential well of noncentral atoms using exafs spectroscopy

### A.I. Lebedev, I.A. Sluchinskaya

Moscow University Physics Bulletin 2005. 60. N 6. P. 58

A new method to determine parameters of a three-dimensional multiwell potential of noncentral atoms from EXAFS data has been proposed. The main features of this approach are the series expansion of a three-dimensional potential in a cluster in displacement degrees with allowance for constraints imposed by lattice-node symmetry and the exact three-dimensional integration of the distribution function in calculation of EXAFS spectra. Within the framework of this approach, parameters of a multiwell potential were estimated for the first time in classical approximation for a Ge atom in solid solution Sn$_{1-x}$Ge$_x$Te ($77\le T\le300$ K, $x\ge0.4$). It is shown that the anharmonic part of the potential is strongly anisotropic and that by its type a ferroelectric phase transition in Sn$_{1-x}$Ge$_x$Te is intermediate between the displacement and order—disorder transitions.

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Theoretical and mathematical physics

## Spectral problem for a waveguide with impedance boundary conditions

### A.N. Bogolyubov, M.D. Malykh, Yu.V. Mukhartova

Moscow University Physics Bulletin 2005. 60. N 6. P. 70

Normal waves in a hollow cylindric waveguide Ω with a smooth-boundary cross section S have been considered. The Shchukin—Leontovich boundary conditions at the waveguide boundary were specified. It has been demonstrated that the propagation constant cannot be purely real in this system.

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## Classical solutions of equations of the (2+l)-dimensional gauge field model

### V.Ch. Zhukovskii, A.M. Fedotov

Moscow University Physics Bulletin 2005. 60. N 6. P. 65

Basing upon the proposed method of numerical solutions of classical field equations, various modes of behavior of classical non-Abelian gauge fields have been studied in a (2+l)-dimensional space-time with consideration for the contribution of the Chern-Simons topological term and interaction with the Higgs fields.

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