# Issue 5, 2024

## On the set of locally equilibrium configurations of the potential energy of a multiatomic cluster

## On the set of locally equilibrium configurations of the potential energy of a multiatomic cluster

### K. E. Plokhotnikov

The paper studies the question of the set (uniqueness) of locally equilibrium configurations of the potential energy of a multiatomic cluster. A molecular system consisting of many, generally speaking, different atoms is called a multiatomic cluster. A formalism is proposed for constructing the entire line of multiparticle potentials to describe an arbitrary molecular system. The concepts of “shape matrix” or “morph” for each of the multiparticle potentials are intro-duced and discussed. The algorithm for constructing the potential energy function of a multia-tomic cluster is determined so that one could talk about building a well-defined configuration of cluster atoms as the only possible one. This algorithm is considered as a way to solve the problem of choosing the configuration of cluster atoms as locally equilibrium. The sets of locally equilibrium configurations of binary and multiparticle potentials are studied in detail. A set of locally equilibrium configurations of a linear combination of binary and multiparticle potentials is also considered. It is shown that in the latter case, the set of locally equilibrium configurations is determined mainly by the binary potential. The general constructions and conclusions are illustrated by examples of reproduction as locally equilibrium standard configurations of water, methane, ethylene and benzene molecules. Suitable potentials are constructed having the specified configurations as global minima. Using examples of the description of clusters of water, benzene and carbon, the question of the causes of the appearance of a variety of locally equilibrium con-figurations is investigated. An algorithm for constructing a complex, composite shape matrix for clusters consisting of many identical molecules is discussed. The use of the concept of “shape matrix” allows us to naturally take into account all possible integral subunits in the molecular system, as well as describe the limits within which these wholes are reproduced unchanged.

Show Abstract## Calculation of acousto-optic figure of merit and maximum value of elasto-optic constant of liquids

## Calculation of acousto-optic figure of merit and maximum value of elasto-optic constant of liquids

### P. A. Nikitin

The elastic-optical properties of liquids based on the grounds of acousto-optics are theoretically investigated. A relation for evaluation of the elastic-optical constant of liquids using only the index of refraction is obtained. The refractive index values maximizing the elastic-optic constant of polar and nonpolar liquids are determined. Calculations are performed for about 100 liquids and compared with known experimental data. This study significantly expands understanding of the acousto-optic effect and has practical use for predicting the elastic-optical constant of liquids and evaluation its wavelength dispersion.

Show Abstract## Determination of collision centrality using the MPD/NICA hadron calorimeter based on Bayes' theorem

## Determination of collision centrality using the MPD/NICA hadron calorimeter based on Bayes' theorem

### N. A. Kurepin$^1$, L. A. Jakobnuk$^3$, V. S. Popov$^3$, A. B. Kurepin$^2$

Determination of collision centrality for heavy nuclei is necessary for any of the planned experiments at the MPD installation of the NICA collider at JINR. In a number of studies at high energies at the RHIC and LHC colliders, good results were obtained using the registration of spectators by forward hadron calorimeters. However, at intermediate energies at NICA of 2.5 – 5.5 GeV per nucleon, due to the insufficient intrinsic resolution for the released energy of the calorimeter, the problem should be studied in more details. In this work, based on Bayes' theorem, resolution estimates are obtained for the impact parameter (centrality), which differ from the results of direct modeling of the calorimeter with a fixed number of spectators.

Show Abstract## Calculation of the energy and angular distributions of secondary particles arising from proton beam irradiation

## Calculation of the energy and angular distributions of secondary particles arising from proton beam irradiation

### I. F. Zharinov$^1$, A. A. Shcherbakov$^{1,2}$, F. R. Studenikin$^{1,2}$

Recently, proton radiation therapy has become widespread as an effective treatment for various oncological diseases. Due to the interaction of protons with matter, a significant number of secondary particles are formed. The article examines the secondary particles that arise during proton therapy. An additional dose load outside the irradiated area is considered. Spectral, dose, and angular distributions of secondary neutrons are calculated. Calculations are performed using the GEANT4 software package. Based on the simulation results, graphs are constructed, conclusions are drawn based on them about the preferred directions of secondary neutron propagation and possible risks for people near a working accelerator are estimated. The results obtained allow us to conclude about possible health risks, as well as the need to improve safety regulations for proton radiation therapy.

Show Abstract## Application of correlation analysis of terahertz spatial light modulator patterns to improve the quality of ghost imaging

## Application of correlation analysis of terahertz spatial light modulator patterns to improve the quality of ghost imaging

### T. V. Blagova, I. S. Khasanov

Terahertz (THz) radiation has unique properties that make it promising for a wide range of applications, including medical diagnostics, non-destructive testing, and security. However, existing multi-pixel cameras have limitations in sensitivity and resolution. The ghost imaging (GI), which utilises a single-pixel detector and a spatial light modulator (SLM), makes it possible to overcome these limitations. One of the features of THz SLM is that the pixel size is comparable to the wavelength, which can lead to significant diffraction distortions. In order to improve the quality of the reconstructed images, this work optimizes the ghost imaging method using correlation analysis of terahertz spatial modulator patterns. In particular, the efficiency of the selection of lighting patterns based on various orthogonal matrices, such as discrete Fourier transform, discrete cosine transform, Hadamard transform and Haar transform, is analyzed. It is also shown that correlation analysis enables the selection of subpixel scanning strategy for super-resolution imaging. Thus, it is shown that correlation analysis is an effective way to evaluate the quality of optical systems for ghost imaging.

Show Abstract## Determination of the parameters of multilayer impurity semiconductor-type carbon nanotubes based on the analysis of conductivity in static and alternating electric fields

## Determination of the parameters of multilayer impurity semiconductor-type carbon nanotubes based on the analysis of conductivity in static and alternating electric fields

### S. Yu. Glazov, N. E. Mescheryakova, I. A. Podgornaya

The paper proposes an analytical method for determining the parameters of multilayer impurity carbon nanotubes of semiconductor type (number of layers, their radii, depth of impurities and their concentration) based on a comparison of experimental and theoretical dependences of current strength on the characteristics of external static and alternating electric fields. The density of the electric current generated in a carbon nanotube under the action of external electric fields is calculated using the kinetic Boltzmann equation. The quasi-classical imaginary time method was used to describe the ionization of atoms.

Show Abstract## Simulation of diffraction patterns on poly- and single crystals in the special courses and cours of laboratory work and of the Department of Solid State Physics, Faculty of Physics, Moscow State University

## Simulation of diffraction patterns on poly- and single crystals in the special courses and cours of laboratory work and of the Department of Solid State Physics, Faculty of Physics, Moscow State University

### A. G. Khundjua$^1$, E. A. Brovkina$^1$, M. M. Melnikov$^2$

The complex of modeling diffraction patterns developed at the Department of Solid State Physics of the Faculty of Physics of Lomonosov Moscow State University is considered. The complex includes several sections: 1) diffraction on polycrystals - tasks for the construction and analysis of diffraction pattern on polycrystalline samples; 2) diffraction on single crystals - modeling and analysis of electron diffraction and Laue patterns; 3) modeling of point patterns of diffraction on two-phase crystalline objects related by orientation ratio (including martensitic transformations). Various options for using computer programs for a course of laboratory work and special courses of the department are discussed.

Show Abstract## The Klein Paradox and Klein Tunneling

## The Klein Paradox and Klein Tunneling

### A. I. Ternov

An interpretation of the Klein paradox is given on the basis of the single-particle approximation of the Dirac theory. The Klein paradox for the Dirac electron and Klein tunneling for charge carriers in graphene are considered from a unified point of view. The close connection between the phenomenon of "retrograde motion" in relativistic quantum mechanics and the propagation of waves in "left-handed" media in electrodynamics is emphasized. This methodological material is used in teaching the quantum mechanics course at the Moscow Institute of Physics and Technology.

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