Том 124, № 3 (2017)

An expression for the binding energies of electrons in the ground state of an atom is derived on the basis of the Bohr–Sommerfeld quantization rule within the Thomas–Fermi model. The validity of this relation for all elements from neon to uranium is tested within a more perfect quantum-mechanical model with and without the inclusion of relativistic effects, as well as with experimental binding energies. As a result, the ordering of electronic levels in filled atomic shells is established, manifested in an approximate atomic-number similarity. It is proposed to use this scaling property to analytically estimate the binding energies of electrons in an arbitrary atom.

We have described the method of analyzing and reporting on the results of calculation of the small-angle structure of radiation scattered by a polymer-dispersed liquid crystal film with electrically controlled interfacial anchoring. The method is based on the interference approximation of the wave scattering theory and the hard disk model. Scattering from an individual liquid crystal droplet has been described using the anomalous diffraction approximation extended to the case of droplets with uniform and nonuniform interface anchoring at the droplet–polymer boundary. The director field structure in an individual droplet is determined from the solution of the problem of minimizing the volume density of the free energy. The electrooptical effect of symmetry breaking in the angular distribution of scattered radiation has been analyzed. This effect means that the intensities of radiation scattered within angles +θ_s and–θ_s relative to the direction of illumination in the scattering plane can be different. The effect is of the interference origin and is associated with asymmetry of the phase shift of the wavefront of an incident wave from individual parts of the droplet, which appears due to asymmetry of the director field structure in the droplet, caused by nonuniform anchoring of liquid crystal molecules with the polymer on its surface. This effect is analyzed in the case of normal illumination of the film depending on the interfacial anchoring at the liquid crystal–polymer interface, the orientation of the optical axes of droplets, their concentration, sizes, anisometry, and polydispersity.

The generation of coherent optical phonons in a polycrystalline antimony film sample has been investigated using femtosecond electron diffraction method. Phonon vibrations have been induced in the Sb sample by the main harmonic of a femtosecond Ti:Sa laser (λ = 800 nm) and probed by a pulsed ultrashort photoelectron beam synchronized with the pump laser. The diffraction patterns recorded at different times relative to the pump laser pulse display oscillations of electron diffraction intensity corresponding to the frequencies of vibrations of optical phonons: totally symmetric (A_1g) and twofold degenerate (E_g) phonon modes. The frequencies that correspond to combinations of these phonon modes in the Sb sample have also been experimentally observed.

We study the transverse momentum spectra of identified pions (π^– + π⁺), kaons ((K^– + K⁺), K₀^s), protons (p + p̅) and lambda hyperons (Λ + Λ̅) produced at mid-rapidity (0 < y_cm < 0.5) in most central (0‒5)% p–Pb collisions at \(\sqrt {s_{NN} }\) = 5.02 TeV in comparison with a Unified Statistical Thermal Freeze-out Model (USTFM). The measurements for pions are reported upto p_T = 3 GeV, the kaons (K^– + K⁺) are reported upto p_T = 2.5 GeV, K₀^s is reported upto p_T = 7 GeV, and the baryons (protons and lambda hyperons) are reported upto p_T = 3.5 GeV. A good agreement is seen between the calculated results and the experimental data points taken from the ALICE experiment. The transverse momentum spectra are found to be flatter for heavy particles than for light particles. Bulk freeze-out properties in terms of kinetic freeze-out temperature and the transverse collective flow velocity are extracted from the fits of the transverse momentum spectra of these hadrons. The effect of resonance decay contributions has also been taken care of.

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric and cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g₀₀ = 0 or g₀₀ = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.

An analytical model has been developed to describe the influence of solute trapping during rapid alloy solidification on the components of the Gibbs free energy change at the phase interface with emphasis on the solute drag energy. For relatively low interface velocity V < V_D, where V_D is the characteristic diffusion velocity, all the components, namely mixing part, local nonequilibrium part, and solute drag, significantly depend on solute diffusion and partitioning. When V ≥ V_D, the local nonequilibrium effects lead to a sharp transition to diffusionless solidification. The transition is accompanied by complete solute trapping and vanishing solute drag energy, i.e. partitionless and “dragless” solidification.

The structural and magnetic properties of the mesoporous systems based on silicon dioxide with a regular hexagonal arrangement of pores several microns in length and several nanometers in diameter, which are filled with iron compound nanofilaments in various chemical states, are studied in detail. The studies are performed using the following mutually complementary methods: transmission electron microscopy, SQUID magnetometry, electron spin resonance, Mössbauer spectroscopy, polarized neutron small-angle diffraction, and synchrotron radiation diffraction. It is shown that the iron nanoparticles in pores are mainly in the γ phase of Fe₂O₃ with a small addition of the α phase and atomic iron clusters. The effective magnetic field acting on a nanofilament from other nanofilaments is 11 mT and has a dipole nature, the ferromagnetic–paramagnetic transition temperature is in the range 76–94 K depending on the annealing temperature of the samples, and the temperature that corresponds to the change in the magnetic state of the iron oxide nanofilaments is T ≈ 50–60 K at H = 0 and T ≈ 80 K at H = 300 mT. It is also shown that the magnetization reversal of an array of nanofilaments is caused by the magnetostatic interaction between nanofilaments at the fields that are lower than the saturation field.

The dependences of the electrical resistivity and the Hall coefficient of single-crystal p-InAs〈Mn〉 bulk samples with an acceptor concentration of about 10¹⁸ cm^–3 on uniform pressure P = 4–6 GPa at T = 300 K in the region of impurity conduction are quantitatively analyzed. The anomalous Hall effect is shown to occur in p-InAs〈Mn〉. Its contribution is negative and correlates with the deionization of acceptors and an increase in the magnetic susceptibility.

Dusty plasma structures in glow discharge in helium in the temperature range of 5–300 K are investigated experimentally. We have described the experimental setup that makes it possible to continuously vary the temperature regime. The method for experimental data processing has been described. We have measured interparticle distances in the temperature range of 9–295 K and compared them with the Debye radius. We indicate the ranges of variations in experimental parameters in which plasma–dust structures are formed and various types of their behavior are manifested (rotation, vibrations of structures, formation of vertical linear chains, etc.). The applicability of the Yukawa potential to the description of the structural properties of a dusty plasma in the experimental conditions is discussed.