Faculty of Physics
M.V.Lomonosov Moscow State University

# Выпуски журнала

## Massless quasi-particle in a constant magnetic field and electromagnetic wave in graphene

### I. S. Durandina, V. C. Zhukovsky

Memoirs of the Faculty of Physics 2019. N 6.

The motion of an electron in graphene in a magnetic field in the presence of an external electromagnetic wave of circular polarization is studied. Electron in graphene has linear momentum energy spectrum corresponding to the dispersion law for massless quasiparticles. The solution corresponding to cyclotron resonance when a frequency of radiation coincides with a  cyclotron frequency '' of quasiparticles in the absence electromagnetic wave is obtained in the limit of a weak field. Since a rotational frequency of massless quasiparticles in magnetic field depends on its energy a cyclotron resonance line turns out to be very broad. For the special case, where the frequency of radiation is twice the  cyclotron '' frequency, the exact solution of the equation of motion of quasiparticle in a magnetic field and field of the wave is obtained. Thus in this case in terms of describing the electron motion we obtain a kind of the wave frequency halving in a magnetic field.

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## Analysis of the criterion for the selection of gamma rays by angular distribution of Cherenkov light for experiment "Pamir-XXI"

### R. -. Bakhromzod$^1$, V. I. Galkin$^2$

Memoirs of the Faculty of Physics 2019. N 6.

Criteria are analyzed for the selection of gamma-ray showers against the background of proton showers. The mechanism of criterion functioning is described in the primary energy range 30-100 TeV. The basis of a criterion capable of separating the two classes of events is formed by the integrals of the optical cascade curve over the characteristic altitude ranges which are obtained through the measured angular distribution of Cherenkov light of an extensive air shower. The conducted analysis gives way to further improvements of criteria for Cherenkov gamma-ray astronomy and the study of mass composition of the primary cosmic rays.

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## Analysis of the shape evolution phenomena in $^{96}$Zr and $^{96}$Mo based on the collective Bohr Hamiltonian

### M. A. Mardyban$^{1,2}$, D. A. Sazonov$^{1,2}$, T. M. Shneydman$^1$, E. A. Kolganova$^{1,2}$, R. V. Jolos$^{1,2}$

Memoirs of the Faculty of Physics 2019. N 6.

The observed properties of the low-lying collective excitations of $^{96}$Zr and $^{96}$Mo are investigated in the framework of the collective quadrupole nuclear model with the Bohr Hamiltonian, whose potential energy has two minima – spherical and deformed. Satisfactory description of the excitation energies and transition probabilities is obtained. It is shown that in the case of $^{96}$Zr both minima are sufficiently deep. However, in the case of $^{96}$Mo a deformed minimum is only outlined.

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## The program for calculating the electrodynamic system of the klystron using the equivalent circuit of a ring resonator working with E0n0 mode

### R. A. Kosarev, I. A. Freydovich

Memoirs of the Faculty of Physics 2019. N 6.

The article discusses the results of the development of a one-dimensional disk mathematical model of the electrodynamic system of a multi-beam klystron, taking into account the non-identical conditions for the interaction of electron beams with the fields of ring resonators. An equivalent circuit of a ring resonator operating on the highest form of oscillations is presented, based on the equations of electromagnetic wave propagation in a waveguide with losses and adequately tracking the amplitude and phase unevenness of the microwave field in the ring gaps of the resonator interaction. The unevenness of the field in the interaction gap can be caused by the influence of communication elements with the load, unequally grouped electron beams and other factors.

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## The results of the study of the radiation resistance of organic scintillators based on polystyrene and polyvinyltoluene

### V. V. Ustinov, E. V. Sukhov, S. V. Afanasiev, D. G. Sakulin

Memoirs of the Faculty of Physics 2019. N 6.

There were studies the radiation resistance of organic plastic scintillators UPS-923A, SCSN-81, SC-301 and SC-307 based on polystyrene, and scintillators BC-408 and EJ-260 based on polyvinyl toluene. There were also studied properties of irradiated Tyvek and ESR reflectors; Paint + TiO2, PMS + TiO2 and Epoxy + TiO2 coatings. The results of this work are aimed at the creating of a radiation-resistant CMS Hadron Endcap Calorimeter at the Large Hadron Collider. The CMS detector is currently being upgraded to study the Higgs boson under the high luminosity conditions.

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## The limiting transition from the Poisson distribution to the Gauss distribution for physicists

### O. A. Chichigina, V. M. Petnikova

Memoirs of the Faculty of Physics 2019. N 6.

Poisson distribution is derived from gamma-distribution. The passage to the limit for sufficiently large values of parameter to normal distribution is proved without using Stirling's formula. Results are illustrated on the example of Brownian particle motion.

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## General harmonic solution of the equations of dilaton-Maxwell electrodynamics

### O. V. Kechkin$^1$, P. A. Mosharev$^2$

Memoirs of the Faculty of Physics 2019. N 6.

The paper presents a general harmonic solution of Maxwell's electrodynamics equations with a dilaton in the stationary case. One of the presented classes of solutions describes the field of a dione with a nontrivial dilaton charge. It is shown that for a harmonic solution of the Coulomb type, the magnetic field is purely Coulomb, whereas the electric and dilaton fields can be distributed in space in a complex way.

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## The effect of the structure on the optical properties of epicular blue spruce wax (Picea pungens)

### E. R. Bukhanov$^1$, A. V. Shabanov$^1$, M. N. Krakhalev$^1$, M. N. Volochaev$^1$, Yu. L. Gurevich$^2$

Memoirs of the Faculty of Physics 2019. N 5.

The study of morphological and optical characteristics of the epicular wax layer of blue spruce (Picea pungens). The method of scanning electron microscopy revealed structural units - tubes with a diameter of 150-200 nm and a length of 3-5 microns. An iridescence effect from the wax layer domains has been detected. In the reflected light, the domains have a blue color, when observed in transmitted light acquire a pinkish tint. These optical characteristics are the main features of the photonic crystal structure. A numerical simulation of the transmission spectrum with the identified structural optical parameters was carried out using the transfer matrix method. The spectrum of the maximum fluorescence coincides with the defect mode of the calculated transmission spectrum.

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## Numerical modeling, visualization, and counting of the velocity of shear waves in soft biological tissues

### A. A. Lisin, S. N. Gurbatov, I. Yu. Demin, A. E. Spivak

Memoirs of the Faculty of Physics 2019. N 5.

This article focuses on the use of the Westervelt equation for solving problems in a medical application. A numerical simulation of the ultrasonic wave propagation in space, close to soft biological tissues was carried out, the SWEI mode of operation was modeled, and the shear wave velocity was obtained for media repeating calibrated CIRS phantoms based on the simulation results. The results were compared with the results on the Verasonics research system.

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## On the drift properties of the Stokes wave packet propagating along an electrically charged interface between liquid media

### A. A. Ochirov, D. F. Belonozhko

Memoirs of the Faculty of Physics 2019. N 5.

The analytical asymptotical expretions of velocity of drift flow and expressions for trajectories of individual liquid particles are derived for system of two immiscible liquids shifting with relate to each other along the electrically charged interface with the Stokes's wave paket propogating along the interface.

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