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

## Perturbativity and nonperturbativity in large-$Z$ effects for hydrogen-like atoms

### K.A. Sveshnikov$^1$, D.I. Khomovsky$^2$

Moscow University Physics Bulletin 2016. 71. N 5. P. 465

The effects induced by the interaction $\Delta U_{AMM}$ of the anomalous component of the electron magnetic moment with the Coulomb field of a nucleus at Zα > 1 are examined for the lower levels of a hydrogenlike atom within purely perturbative and essentially nonperturbative in α/π approaches. Owing to the specific features of the $\Delta U_{AMM}$ operator for a point-like Coulomb source, the distribution of the charge over the volume of the nucleus is set in the nonperturbative case at the quark structure level using valence (constituent) u and d quarks. It is demonstrated that such nonperturbative analysis turns out to be nontrivial as well as the manner in which its results are altered in the transition from the central problem with spherical symmetry to the inclusion of the peripheral contribution. It is also demonstrated that these methods yield matching (with an accuracy no worse than 0.1%) results for the shift of levels$1s_{1/2}$ and $2p_{1/2}$ due to $\Delta U_{AMM}$ at all values of Z through to critical ones. Thus, it is confirmed that the perturbation theory in α/π provides correct results for superheavy atoms if the complete dependence of the wave function on Zα is taken into account from the beginning.

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Condensed matter physics

## Effect of Incidence Angle on the Electrical Parameters of Vertical Parallel Junction Silicon Solar Cell under Frequency Domain

### Gökhan Sahin

Moscow University Physics Bulletin 2016. 71. N 5. P. 498

The effect of incidence angle on the electrical parameters of vertical parallel silicon solar cell under frequency domain was theoretically analyzed. Based on the diffusion-recombination equation, the expression of excess minority carrier density in the base was established according to the modulation frequency and the illumination incidence angle. The excess minority carrier density, the photocurrent density, the photovoltage, series resistance, shunt resistance, electric power and the space charge region capacitance were calculated and plotted. The objective of this work was to show the effects of solar cell modulation frequency and the illumination incidence angle on these electrical parameters, electric power and space charge region capacitance. Plots of solar cell’s electric power with the junction recombination velocity gave the maximum solar cell’s electric power; Pm. Influence of various parameters of incidence angles on the solar cell’s electric power was also studied.

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## Classification of phenomenological phase transition models by the methods of equivariant catastrophe theory: models with $L=C_{nv}$ $(n=3, 4, 6)$

### S.V. Pavlov

Moscow University Physics Bulletin 2016. 71. N 5. P. 508

A classification of phenomenological phase-transition models for the two-component order parameter by the methods of equivariant catastrophe theory is proposed. The models are constructed on the basis of the number of thermodynamic parameters that are varied in an experiment (temperature, pressure, chemical potentials of admixtures, etc.) instead of the simple expansion of the thermodynamic potential in an order parameter power series. The classification of models with the order parameter symmetry groups $L=C_{nv}$ $(n=3, 4, 6)$ with the number of varied parameters from 1 to 5 is performed.

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Theoretical and mathematical physics

## The interaction energy of three molecules united in a nanocluster by long-range attraction forces with account for Coulomb repulsion

### V.V. Komarov$^{1,2}$, A.M. Popova$^{1,2}$, L. Schmidt$^{2}$, H. Jungclas$^{2}$

Moscow University Physics Bulletin 2016. 71. N 5. P. 476

The interaction energy of three neutral molecules that form a nanocluster is studied. It is assumed that one molecule (M$_0$ ) has a dipole moment, while the other two (M$_1$ and M$_2$ ) are nonpolar. The molecule interaction energy in such a nanocluster is determined by the sum of dispersion interaction energies of each pair of molecules and the sum of inductive energies of the molecules. Analytical expressions for these energies as functions of the distance between the centers of mass of the molecules have been obtained. A method for the determination of damping functions which takes the contribution of repulsive forces into account has been developed. Analytical expressions for the molecule interaction energies for a two-molecule cluster in an external field of the third molecule have been obtained. A nanocluster consisting of a molecule of polar isomer pentene C$_5$H$_{10}$ and a nonpolar molecule of polycyclic aromatic hydrocarbon pyrene C$_{16}$H$_{10}$ in the external electrostatic field of another pyrene molecule is considered. The calculation showed that the interaction energy of the two-molecule nanocluster increases by a factor of 1.5 if this cluster is in the field of the induced dipole moment of an external pyrene molecule.

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Optics and spectroscopy. Laser physics

## "Weak" measurements and supraluminal communication

### A.V. Belinsky, A.K. Zhukovsky

Moscow University Physics Bulletin 2016. 71. N 5. P. 482

A modified experiment with a correlated pair of particles in an entangled space is suggested. The experiment demonstrates that for weak and/or nondemolition measurements of one of the particles, information can be transmitted at a speed that is not limited by the speed of light.

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## On the phase uncertainty of Fock states and <<nonlocal realism>>

### A.V. Belinsky

Moscow University Physics Bulletin 2016. 71. N 5. P. 487

Based on the study of the effects of the suppression of cross-correlation of photons on a beam splitter and preparation of squeezed states, an experimental proof is proposed for the lack of determinate values of the phase and phase difference of photons in Fock states. It is shown that this conclusion unveils the intrinsic inconsistency of interpreting quantum mechanics on the basis of the nonlocal theory of hidden variables and proves the inadequacy of the latter.

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## Analyzing the effect of nonlocality on the scattering properties of a plasmonic nanocylinder using the discrete-source method

### Yu.A. Eremin$^1$, A.G. Sveshnikov$^2$

Moscow University Physics Bulletin 2016. 71. N 5. P. 492

The problem of the diffraction of the field of a plane electromagnetic wave by a metal nanocylinder with an arbitrary cross section is considered. Based on the discrete-source method, a comparative analysis of both frequency and spatial scattering characteristics is performed taking the nonlocal effect into account. It is found that nonlocality produces a substantial effect on the scattering characteristics. It is demonstrated that the use of the Drude model for a refractive index of plasmonic particles in the ultraviolet region may lead to erroneous results.

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Biophysics and medical physics

## Estimation of the permissible time for human presence in the zone of an emergency release of uranium hexafluoride with inhalation

### S.P. Babenko$^1$, A.V. Badin$^2$, A.V. Ovchinnikov$^2$

Moscow University Physics Bulletin 2016. 71. N 5. P. 514

This paper describes a complex model that allows one to calculate the mass of harmful substances that enter the human body in the conditions of an emergency release of uranium hexafluoride (UF$_6$ ) in a work space. It covers all parts of the process, from the pollution of the work environment by gaseous UF$_6$ , before the penetration of toxic substances in the body. The model is built based on the available data in the literature about the research on this subject. On the basis of numerical calculations carried out within the framework of the constructed model it is concluded that the predominant harmful role belongs to inhalation. It shows the relationship between the residence time in an emergency and the amount of fluorine taken into the body, which is the most toxic to humans. The allowable residence time of a person in an emergency release zone is estimated.

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Physics of Earth, atmosphere, and hydrosphere

## The horizontal motion of a water layer during the passage of tsunami waves based on data from a dense ocean-floor network of deepwater sea-level stations

### G.N. Nurislamova, M.A. Nosov

Moscow University Physics Bulletin 2016. 71. N 5. P. 520

A method for the retrieval the horizontal motion of a water layer during the passage of a tsunami wave is proposed based on the data from a dense network of sea-level deepwater stations. The method is applied for calculation of the horizontal velocity of the flow and displacement of water particles in the vicinity of the DONET/JAMSTEC observatories during the passage the 2011 Tohoku tsunami. It was found that the amplitude of the flow speed was  0.01 m/s, while the amplitude of the displacement exceeded 10 m.

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