Faculty of Physics
M.V.Lomonosov Moscow State University
Physics of nuclei and elementary particles

## Nuclear spectroscopy of $^{40-48}$Ca isotops

### B.S. Ishkhanov$^{1,2}$, M.E. Stepanov$^{1,2}$, T.Yu. Tretyakova$^2$

Moscow University Physics Bulletin 2014. 69. N 6. P. 433

The nature of the excited states of the $^{40-48}$Ca isotopes is analyzed in the region of energies below the nucleon separation threshold. A peculiar feature of the $^{40-48}$Ca isotopes is the predominant filling of the $1f_{7/2}$ neutron shell. Interaction between the neutrons of the $1f_{7/2}$ shell and the nucleons of the $1d2s$ core results in formation of multiparticle excited states with a few vacancies in the $1d2s$ shell. The energies of single-particle proton states in the $^{40-48}$Ca isotopes are calculated using the Hartree-Fock potential with the Skyrme potential. The manner in which the energy of single-particle states varies, the magic numbers $N=20, 28$ are formed, and the charge and nucleon density vary in the $^{40-48}$Ca isotopes as the neutron number increases from 20 to 28 is shown. Coherent interactions of the $1f_{7/2}$ shell and $1d2s$ core nucleons also manifest themselves in the region above the nucleon separation threshold, leading to the configuration and isospin splitting of the GDR.

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Condensed matter physics

## Quantum ground states of copper nitrates

### O.S. Volkova$^{1,2}$, A.N. Vasiliev$^{1,2}$, V.V. Khovailo$^{3,4}$

Moscow University Physics Bulletin 2014. 69. N 6. P. 457

Low-temperature study of matter provides a key to understanding its fundamental properties. Under conditions where thermal fluctuations do not mask fine interactions, quantum cooperative phenomena that have no analogy in classical physics come into play. Among them are superconductivity, low-temperature exotic magnetism, spin and charge density waves, and Bose-Einstein condensation, which are the most important issues for modern condensed-matter physics. Study of the quantum ground states is illustrated by the example of transition metal nitrates in which magnetically active ions form lower-dimensionality frameworks, including dimers, chains, spin ladders, and 2D planes.

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Theoretical and mathematical physics

## On one possible method for Casimir pressure renormalization within a sphere

### A.I. Dubikovsky$^1$, P.K. Silaev$^2$, O.D. Timofeevskaya$^2$

Moscow University Physics Bulletin 2014. 69. N 6. P. 468

We propose a method for Casimir pressure renormalization for a massive scalar field within a sphere. This method differs somewhat from the commonly used one. An alternative method of choosing the normalization point leads not to an inverse polynomial dependence of pressure on the field mass, but to an exponential one. The proposed method does not use scalar fields quantized in the exterior region and thus allows one to circumvent the difficulties that are associated with the standard approach.

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## Classical electrodynamics of an accelerated extended charge

### M.B. Ependiev

Moscow University Physics Bulletin 2014. 69. N 6. P. 474

The extent of an electric charge is considered under the assumption that the structure of the charge at rest is spherically symmetric and the current vector has a linear dependence on the acceleration. An exact expression for the electromagnetic field of the charge is obtained that depends on the specific form of the charge distribution. For the cases when the particle velocity does not considerably change over the time it covers the distance of the order of its own size, approximations are developed that depend on the charge distributions through its low-order momentums. The Lorentz-Abraham-Dirac expression is rigorously proven for radiation friction: the initial expression and the conditions under which the expression can be derived are identified. The radiation field is also studied and it is demonstrated that in some cases of great accelerations the radiation virtually vanishes. Methods for the further development of the theory are pointed out as applied to more general forms of the current vector (dependence of the charge structure on the acceleration, consideration of random factors, etc.)

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## Time-dependent Bell inequalities in a Wigner form

### N.V. Nikitin$^1$, V.P. Sotnikov$^1$, K.S. Toms$^2$

Moscow University Physics Bulletin 2014. 69. N 6. P. 480

We propose time-dependent Bell inequalities in a Wigner form, which expand the possibilities of experimental verification of Bohr’s principle of complementarity in the relativistic domain and for nonstationary quantum-mechanical systems. Derivation of the proposed inequalities is based entirely on the Kolmogorov axiomatics of probability theory and the locality hypothesis. Violation of the obtained inequalities is considered in the framework of quantum theory based on the example of oscillations of neutral B mesons.

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## A hydrodynamic approach to modeling the space charge problem

### E.E. Perepelkin$^1$, N.G. Inozemtseva$^2$, N.P. Repnikova$^1$, M.B. Sadovnikova$^1$

Moscow University Physics Bulletin 2014. 69. N 6. P. 488

A new model is suggested to investigate the influence of a beam charge on the evolution of the charge-density distribution function. The spherically symmetric charge-density distribution of a beam acting on an external homogeneous constant electric field is considered. A new nonlinear boundary problem that takes the influence of a beam’s electric field on the evolution of the charge-density distribution function into account is formulated. The solutions of such a problem can be used as tests in calculation methods that are applied in practice.

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## On new exact solutions to the problem of electrostatics of conductors

### P.A. Polyakov, N.E. Rusakova, Yu.V. Samukhina

Moscow University Physics Bulletin 2014. 69. N 6. P. 493

A new class of conducting figures that allow an analytical solution of a main task of electrostatics was found. Analytical formulas for the surface density of the charge for three figures of this class were obtained.

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## A mathematical model of convective cell motion in the mantle under exposure to a heat source at the mantle-core boundary

### A.N. Bogolyubov$^1$, A.N. Grushinsky$^2$, Yu.V. Mukhartova$^1$, O.E. Belenkaya$^1$

Moscow University Physics Bulletin 2014. 69. N 6. P. 497

An algorithm for numerically solving the vector problem on the modeling of the convective motion of matter in the Earth’s mantle was built and implemented. A 2-D model of convective cell formation in the mantle was considered with a moving heat source at the boundary with a core that generates an upwelling flow of the mantle substance. The motion of the heat source is possible only along the core-mantle boundary. If the heat source is absent, the system is conservative. The mantle was modeled as an incompressible fluid with constant viscosity.

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Physics of nuclei and elementary particles

## The quadrupole lens and extraction magnets of a compact race-track microtron

### I.Yu. Vladimirov$^1$, N.I. Pakhomov$^1$, V.I. Shvedunov$^1$, Yu.A. Kubyshin$^2$, J.P. Rigla$^3$, V.V. Zakharov$^4$

Moscow University Physics Bulletin 2014. 69. N 6. P. 507

The compact race-track microtron (RTM) with a maximum energy of 12 MeV that is under construction at the Technical University of Catalonia consists of a quadrupole lens for horizontal focusing of the beam and four dipole magnets for the extraction of the beam from the accelerator. The source of the magnetic field in the magnets is a rare-earth permanent magnet (REPM). The main characteristics of the quadrupole lens and the extraction magnets and the procedure for the tuning of their magnetic fields are described.

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## On the theory of electromagnetic interactions of a relativistic electron beam and plasma in a coaxial waveguide in an external magnetic field

### M.V. Kuzelev, E.A. Khapaeva

Moscow University Physics Bulletin 2014. 69. N 6. P. 512

Linear electromagnetic interactions of rectilinear electron beams with magnetoactive plasma in a coaxial waveguide are considered. Dispersion equations are derived and field structures of surface plasma waves in the absence of the electron beam are determined. Dispersion equations of beam waves in the absence of plasma waves are derived. Dispersion equations that describe the interaction of plasma and beam waves are derived. Instability increments in regimes of single-particle and collective Cherenkov effects and irregular Doppler effect are calculated.

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Optics and spectroscopy. Laser physics

## A Sagnac interferometer as a gravitational-wave third-generation detector

### N.V. Voronchev$^1$, Sh.L. Danilishin$^2$, F.Ya. Khalili$^1$

Moscow University Physics Bulletin 2014. 69. N 6. P. 519

It is planned that the next generation of laser interferometric gravitational-wave detectors will surpass the second-generation detectors in amplitude sensitivity in a broad range of frequencies by nearly tenfold. Since the sensitivity will be limited by quantum noise at all frequencies above ∼10 Hz at almost all frequencies, the development of new schemes for detectors that are able to provide the required lowered level of quantum fluctuations is very topical. A velocimeter based on the Sagnac interferometer, which is investigated in this study, is one such scheme and possibly is the most promising among them. We present a complete comparative analysis of the quantum noise of the signal-recycling Sagnac and Mickelson interferometers with frequency-dependent squeezing of the quantum state of light and demonstrate the substantial advantage of the former, both in sensitivity and from the viewpoint of its easier experimental implementation. In particular, we show that the Sagnac scheme is able to surpass even a xylophone configuration of two Michelson detectors in the level of quantum noises and is less tolerant to optical losses in the filter cavity when using frequency-dependent squeezing.

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Condensed matter physics

## The structure of self-accommodation complexes of martensite crystals in alloys with the shape memory effect

### A.G. Khundjua, E.A. Brovkina, M.M. Melnikov, A.G. Ptitsin

Moscow University Physics Bulletin 2014. 69. N 6. P. 529

The internal structure of self-accommodation complexes defined by employed twinning planes of martensite crystals is discussed. A method for the analysis of the possible structure of self-accommodation complexes depending on the symmetry of martensite crystals and the orientation relationships between the lattices of austenite and martensite is proposed.

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Biophysics and medical physics

## Monte Carlo calculation of dosimetry parameters for a brachytherapy source

### A.V. Belousov, A.A. Kalachev, A.S. Osipov

Moscow University Physics Bulletin 2014. 69. N 6. P. 535

This study presents the results of calculations of dosimetry parameters for a $^{169}$Yb model brachytherapy source. The calculations were performed by a program code that was written by the authors using the GEANT4.9 software package for Monte Carlo simulation. According to the AAPM TG-43 formalism (the American Association of Physicists in Medicine, Task Group No. 43), the following parameters were deter- mined: the dose-rate constant, radial dose functions, and anisotropy function. To verify the program code, the calculation of the dosimetry parameters of the widespread BEBIG Co0.A86 and BEBIG Ir2.A85-2 sources was carried out. An acceptable fit with the data of other authors was obtained. The data we obtained using the developed and verified program code could be used in dosimetry planning systems.

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## The physicochemical basis of the biological activity and pharmacological properties of the antiviral agent Panavir

### S.V. Stovbun$^1$, L.V. Yakovenko$^2$

Moscow University Physics Bulletin 2014. 69. N 6. P. 542

The agent Panavir possesses versatile antiviral, anti-inflammatory, and analgesic effects, which still have not been explained at the molecular level. Here, we propose a simple physicochemical model of Panavir nanoparticles, which allows one to explain its effects by the mechanical activation of cells, including those of the immune system. Thus, there is no need for binding of the Panavir particles to any supramolecular chiral receptor for manifestation of its all known effects.

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## An autowave model of vesicle formation on the ocean surface

### V.A. Tverdislov$^1$, L.V. Yakovenko$^1$, M.E. Mazurov$^2$, I.M. Kaluzhny$^2$

Moscow University Physics Bulletin 2014. 69. N 6. P. 548

According to the hypothesis of the origin of life on Earth proposed by the coauthors of this publication [4–6], when an aerosol particle that was generated by bursts of air bubbles on the surface of an ancient ocean and was covered by a monolayer of amphiphile fell back on the surface it was transformed into a vesicle covered by a bilayer of amphiphilic molecules. The vesicle is considered as a cell prototype because it is in a thermodynamically nonequilibrium state caused by asymmetry of the distributions of ions and chiral components. In this work, the ocean surface layer is considered as an active medium that can be described by the Fitzhugh-Nagumo equations. A computational experiment showed that a stable vesicle covered by a bilayer of amphiphilic molecules can be formed under such conditions and that it submerges.

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## Raman spectroscopy of albumin interaction with nanodiamond films

### N.N. Brandt$^1$, R.R. Ismagilov$^1$, A.V. Priezzhev$^{1,2}$, A.S. Svetlakova$^1$, A.Yu. Chikishev$^2$

Moscow University Physics Bulletin 2014. 69. N 6. P. 552

This study is focused on finding the possible structural changes of molecules of one of the principal proteins of blood plasma (albumin) that occur upon their interaction with nanodiamonds. The interaction between nanodiamond films and protein films that form after solutions dry up is analyzed. A possibility of spontaneous protein crystallization after the solution dries up on the surface of a nanodiamond film is demonstrated. It is found by means Raman spectroscopy that the secondary structure, the structure of disulfide bridges, and the structure of the tyrosine doublet of the protein do not change (with respect to the corresponding structures in the lyophilized state) upon the interaction of the protein with a nanodiamond film, at least in the bulk of a protein film with a thickness of 1 μm. However, conformational changes may occur in a fairly thin (about 20 nm) near-surface layer of the protein film.

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Astronomy, astrophysics, and cosmology

## On the mechanism of the formation and mass growth of solar system bodies at the early stages of evolution

### T.R. Abdul’myanov

Moscow University Physics Bulletin 2014. 69. N 6. P. 558

In the present paper, the early evolution of the Solar System with regard to the process of the formation and mass growth of small bodies in protoplanetary rings is considered. This process is modeled with the use of the results that were obtained in the analysis of the libration motions of asteroids. It has been shown that libration centers could occur prior to the formation of the bodies, when the redistribution of gaseous-dust grains occurred in protoplanetary rings. The distribution density of gaseous-dust grains could be similar or equal to that in the Gaussian ring or its analogs for long-period librations. In this case, the bodies can be initially formed and grow in stable libration centers.

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Physics of Earth, atmosphere, and hydrosphere

## The structural stability of the pattern of immiscible fluid transfer in a vortex flow

### T.O. Chaplina$^1$, E.V. Stepanova$^2$, Yu.D. Chashechkin$^2$

Moscow University Physics Bulletin 2014. 69. N 6. P. 565

This is an experimental study of the characteristics of the transport of immiscible admixtures in a composite vortex with a free surface. We examined the evolution of a compact marker spot (sunflower oil and diesel oil) into the spiral arms on a composite vortex surface and the formation of an oil body in the fluid. Common elements in the distribution geometry were identified. The character of the transport of matter was shown to be independent of admixture properties in a wide range of variation in its density and viscosity. The experimentally obtained quantitative regularities of the admixture transport can be used for developing adequate physical and mathematical models of transport processes in vortex flows.

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