R e v i e w s

Physics of nuclei and elementary particles

Moscow University Physics Bulletin 2018. **73**. N 3. P. 243

On the basis of data on proton–proton collisions at the energy √s = 8 TeV and with the integrated luminosity of 19.8 fb−1, the resolution of the transverse momentum and the uncertainty of the energy scale were estimated for jets that were reconstructed using the Jet-Plus-Track algorithm. The performance of the algorithm for the identification of jets that originated from the signal event and the separation of jets into quark and gluon jets was also assessed

Show AbstractOptics and spectroscopy. Laser physics

Moscow University Physics Bulletin 2018. **73**. N 3. P. 252

Four experimental situations are analyzed from the viewpoint of fulfilling the causality principle: instantaneous collapse of the quantum state vector of a system of entangled particles, a quantum eraser, the quantum Zeno paradox, and light transformation by a nonlinear beam splitter. The last is a planar interface of two transparent dielectrics, at least one of which possesses Kerr nonlinearity, that is, its refractive index depends on the intensity of radiation that penetrates it. It has been shown that the causality principle in the first two cases can be violated only in the sense of the instantaneousness of the manifestation of the effect with respect to the cause. For a nonlinear beam splitter, in addition to the directly opposite predictions given by the quantum and classical theories of its description for the behavior of phase fluctuations of the radiation transformed by the splitter, the causality principle is violated in the most general sense: the effect of the following event on the previous one. The quantum Zeno paradox occupies an intermediate position of democratic involvement of the cause and effect in the general cascade of two subsequent events, i.e., the first event can prevent the second event, just as the second event can prevent the first one.

Show AbstractR e g u l a r p a p e r s

Theoretical and mathematical physics

Moscow University Physics Bulletin 2018. **73**. N 3. P. 263

We have obtained equations for calculating the parameters of phase transitions in particle systems with a nonnegatively defined interaction potential. The parametrized Gibbs distribution is part of the basis of our derivation. It takes the features of a non-negatively defined interaction potential into account and leads to the corresponding Bogolyubov chain of equations. Using this approach, we obtain a convenient method for finding the free energy of the system. On the basis of this method, we have studied the phase transition in a system of hard spheres and the dependence of the phase-transition temperature on the temperature of argon at high pressures.

Show AbstractMoscow University Physics Bulletin 2018. **73**. N 3. P. 269

In this paper, the problem of electromagnetic wave diffraction by extensive conducting bodies with uniform cross sections and continuous curvature boundaries is studied. Corrugated cylinders are considered as diffusers. A resonant decrease in the radiation visibility of such bodies was discovered

Show AbstractMoscow University Physics Bulletin 2018. **73**. N 3. P. 278

—We propose a procedure for renormalizing the Casimir energy that makes the steps that are used in the standard renormalization procedure, that is, regularization, subtraction, and deregularization, implicit. The proposed procedure is based on the calculation of a set of convergent sums, each of which is related to the initial divergent sum of the non-renormalized Casimir energy. Next, we construct a system of linear equations that relates this set of convergent sums to the renormalized Casimir energy. The unknown renormalized Casimir energy is obtained as a result of solving this system of equations. In this case, both the calculations of the convergent sums and the subsequent solution of the system of linear equations are performed with a certain (generally speaking, arbitrary) ordered accuracy; thus, the result is also approximate. The proposed procedure is, first, more computationally effective than the standard one, and, second, applicable not only to the problems where a transcendental equation for the spectrum can be written, but also to the problems where the spectrum is known only numerically.

Show AbstractMoscow University Physics Bulletin 2018. **73**. N 3. P. 284

A nonlinear singularly perturbed system of parabolic equations in a two-dimensional domain is considered. The system can be used to simulate the motion of an autowave front in a model of the evolution of urban ecosystems in the case of an inhomogeneous medium whose parameters vary with time. An asymptotic analysis of the problem is performed using methods of the theory of contrast structures. An asymptotic approximation of a front-type solution of the zero and first orders is obtained.

Show AbstractMoscow University Physics Bulletin 2018. **73**. N 3. P. 293

The quantum dynamics of a nonrelativistic neutral massive fermion with an anomalous magnetic moment (AMM) is examined in the external electric field of an infinitely long thin homogeneously charged thread in the plane with a normal directed along the thread. The Hamiltonian of the Dirac–Pauli equation for a neutral fermion with AMM is essentially singular in the considered external field and requires a supplementary extension of the definition in order for it to be treated as a self-adjoint quantum-mechanical operator. All one-parameter self-adjoint extensions of the Hamiltonian of the Dirac–Pauli equation in the considered external field are found in the nonrelativistic approximation. The corresponding Hilbert space of squareintegrable functions, including a singularity point of the Hamiltonian, is specified for each self-adjoint extension of the Hamiltonian. The wave functions of free and bound states, as well as discrete energy levels, are determined by the self-adjoint extension method and their correspondence with similar quantities obtained by the physical regularization procedure is discussed. It is shown that energy levels of bound states are simple poles of the scattering amplitude, which should be extended in definition by introducing the self-adjoint extension parameter into it. Expressions for the scattering amplitude and cross-section, depending on the orientation of the initial-state spin of fermion, are obtained.

Show AbstractPhysics of nuclei and elementary particles

Moscow University Physics Bulletin 2018. **73**. N 3. P. 301

—An approximation has been proposed for the nucleus single-particle density matrix in calculating the exchange component of the mean-field potential in the double-folding model. The method is based on the pseudo-oscillator representation of the density matrix and makes it possible to separate single-particle and internucleon variables, which greatly simplifies and accelerates the process of calculating the mean-field potential. Test calculations based on examples of alpha-particle interactions with $^{12}$C, $^{16}$O, and $^{40}$Ca nuclei have shown the adequacy of the proposed approximation.

Show AbstractOptics and spectroscopy. Laser physics

Moscow University Physics Bulletin 2018. **73**. N 3. P. 306

A simple method for constructing a 2D fractal cluster of nanodendrities formed in the self-organization process of nanoparticles is presented. The relationship between the structural features of dendrite-type lattices and the fractal characteristics of both studied objects and their diffraction patterns is revealed.

Show AbstractCondensed matter physics

Moscow University Physics Bulletin 2018. **73**. N 3. P. 310

An analysis method for atomistic cluster porosity is presented. Porosity and pore radii are calculated from the coordinates of atoms and van der Waals radii. The pore volume is calculated as the maximum volume of a sphere inscribed in a pore. The method is applied to a silicon dioxide thin film prepared by simulation of ion-beam sputtering. The porosity and distribution of pores by radius are calculated. The concentration of pores that are able to contain small molecules is estimated.

Show AbstractMoscow University Physics Bulletin 2018. **73**. N 3. P. 314

The sequential derivation of an expression that describes an X-ray natural circular dichroism (XNCD) signal in the most general case is performed. The obtained expression is used as a basis to consider XNCD signals and their structural origins in copper metaborate CuB2O4 crystals at an incident radiation energy near the K absorption edge of copper and lanthanum–gallium silicate La$_3$Ga$_5$SiO$_{14}$ crystals at an incident radiation energy near the K absorption edge of gallium. It has been demonstrated that the measurements of circularly polarized X-ray absorption spectra in combination with corresponding first-principle calculations provide an efficient method for studying the contributions of crystallographically non-equivalent atoms to the X-ray optical activity of crystals.

Show AbstractMoscow University Physics Bulletin 2018. **73**. N 3. P. 325

The nonlinear field dependences of the hot electron drift velocity have been calculated by means of numerical solution of the Boltzman kinetic equation in two families of nitride semiconductor solid solutions: In$_x$Ga$_{1-x}$N и In$_x$Al$_{1-x}$N. The calculations have been carried out in the electric field up to 30 kV/cm at lattice temperatures of 77 and 300 K, and for electron concentrations of 1 × 10$^{18}$ and 1 × 10$^{19}$ cm$^{–3}$. In the calculations, the composition x has been taken as 0, 0.25, 0.5, 0.75, and 1 for both alloys.

Show AbstractMoscow University Physics Bulletin 2018. **73**. N 3. P. 329

—The phenomenological models of phase transitions for two one-component interacting order parameters have been classified using the methods of the equivariant catastrophe theory. The models have been constructed based on the number of control parameters, which depend on the thermodynamic parameters varied in experiments (temperature, pressure, chemical potentials of impurities, etc.), rather than by simple expansion of the thermodynamic potential in series of order-parameter powers. The models with the order-parameter symmetry group L = C$_{2v}$ are classified in terms of the number of control parameters from two to five. An infinite series of the phenomenological models with biquadratic interaction of the order parameters was also obtained.

Show AbstractBiophysics and medical physics

Moscow University Physics Bulletin 2018. **73**. N 3. P. 334

This study investigates the effect of X-rays on potato tubers to stop their sprouting at different periods of storage. It has been found that there is a connection between the period of storage and the dose of irradiation. To control the quality of the irradiated tubers, the concentration of reducing sugars was measured during the entire experiment and compared to the parameters of non-irradiated potato tubers.

Show AbstractMoscow University Physics Bulletin 2018. **73**. N 3. P. 339

The physical characteristics of the 75Se radionuclide make it a promising gamma radiator for use as a brachytherapy sealed source. This radionuclide combines relatively low-energy photon radiation emitted during decay with a sufficiently long half-life (approximately 120 days) and the possibility of obtaining high specific activity. All this makes this radionuclide attractive for automated injection brachytherapy. The aim of this work was to study the dosimetric characteristics of $^{75}$Se for its potential use in high and medium dose rate brachytherapy. According to the TG-43 formalism, the radial dose function g(r) and the anisotropy function $F(r, \theta)$ are calculated. $^{75}$Se as a radionuclide for sealed source brachytherapy has many advantages over widely used isotopes and can serve as an alternative to iridium sources.

Show Abstract