Vol 122, No 2 (2016)

The problem of the transition radiation of multicharged ions at the interface between two media and in a thin plate under the charge-exchange conditions has been solved. It has been shown that the processes of pickup (or loss) of electrons by accelerated multicharged ions at the interface between two media significantly increases the yield of transition radiation.

The ratio of the cross section for inelastic scattering to the total cross section for scattering of a fast electron by a cluster, depending on the number of atoms in the cluster, is shown to be not a monotonic function. This nonmonotonicity is not related to the well-known nonmonotonic dependences determined, for example, by the magic numbers in the shell model of clusters but is of purely quantum origin: the coherence of elastic electron scattering and the incoherence of inelastic one by a multipartice target.

A method for detecting dark matter axions in which a dc SQUID serves as a detector is proposed. The SQUID is shown to be able to detect the magnetic field perturbations induced by its interaction with axions. The resonance signal appears as a current step in the SQUID current–voltage characteristic. The voltage of the step corresponds to the axion mass, while its height depends on the axion energy density in near-Earth space. The proposed method is aimed at detecting axions with masses m_a ≲ 10^–4 eV, which are of interest for both cosmology and particle physics.

A solution of the Dirac equation for an electron in the field of a point nucleus (Ze) has been obtained as an eigenfunction of the Schrödinger Hamiltonian and the spin projection operator Σ₃. With the use of this solution, the probability W^(ν) of the emission of a neutrino per unit time from a hydrogen-like atom, \((Ze)* \to (Ze) + \nu \bar \nu\), has been calculated for the first time in the first order of the parameter Ze ≪ 1. The probability W^(ν) appears to be rather small, and the corresponding lifetime τ^(ν) = [W^(ν)]^–1 is much larger than the age of the Universe; correspondingly, this process cannot affect the balance of low-energy neutrinos. The smallness of W^(ν) is due not only to the presence of the obvious “weak” factor (Gm_p²)²(m/mp)⁴ in the expression for W^(ν), but also primarily to the “electromagnetic” factor (Zα)¹², which can be revealed only in a particular calculation. It has been argued within quantum electrodynamics with the mentioned wavefunctions that photon emission, (Ze)* → (Ze) + γ, can be absent (analysis of photon emission requires the further development of the method), whereas axion emission, (Ze)* → (Ze) + a, can occur, although the last two effects have not been considered in detail.

A theoretical model is proposed for computing simulations of laser radiation interaction with inhomogeneous foam materials doped with heavy elements and undoped materials. The model satisfactorily describes many experiments on the interaction of the first and third harmonics of a 200 J pulsed PALS iodine laser with low-density porous cellulose triacetate targets. The model can be used to analyze experimental data and estimate the reality of experimental results.

The equilibrium atomic structure and the phonon spectra of a submonolayer (θ = 0.5 monolayer) Ni film deposited on the surface of Cu(100) are calculated using the potentials obtained by the embedded atom method. We consider atomic relaxation, the vibrational state density distribution on Ni and substrate atoms, and polarization of vibrational modes. Variation of the phonon spectrum upon segregation of Cu atoms on the film surface is considered. It is shown that mixing of vibrations of Ni adatoms with vibrations of substrate atoms occurs in the entire frequency range, leading to a frequency shift of the vibrational modes of the substrate and to the occurrence of new vibrational states atypical of a clean surface. The Cu(100)–c(2 × 2)–Ni structure is dynamically stabler when placed in the subsurface layer of the substrate.

The phase field crystal model provides a continual description of the atomic density over the diffusion time of reactions. We consider a homogeneous structure (liquid) and a perfect periodic crystal, which are constructed from the one-mode approximation of the phase field crystal model. A diagram of 2D structures is constructed from the analytic solutions of the model using atomic density functionals. The diagram predicts equilibrium atomic configurations for transitions from the metastable state and includes the domains of existence of homogeneous, triangular, and striped structures corresponding to a liquid, a body-centered cubic crystal, and a longitudinal cross section of cylindrical tubes. The method developed here is employed for constructing the diagram for the homogeneous liquid phase and the body-centered iron lattice. The expression for the free energy is derived analytically from density functional theory. The specific features of approximating the phase field crystal model are compared with the approximations and conclusions of the weak crystallization and 2D melting theories.

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J₁ and J₂, respectively. PTs in these models are analyzed for the ratio r = J₂/J₁ of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J₁ < 0 and J₂ < 0 exhibits a first-order PT in the range of 0 ⩽ r < 0.2, whereas, in the interval 0.2 ⩽ r ⩽ 1.0, frustrations arise in the system. At the same time, for J₁ > 0 and J₂ < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.

A transition to the surface superconducting state is detected in lead single crystals at a temperature approximately 0.25 mK higher than the bulk superconducting transition temperature. The (H, T) phase diagram of this state is analyzed.

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f(R) gravity. We extend the work on static plane-symmetric vacuum solutions in f(R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f(R) models.

The expressions for the energy spectra of monolayer, bilayer, and multilayer graphene, as well as epitaxial graphene, are derived using the quantum Green’s functions method. Analytic expressions are obtained for the densities of states of these systems. It is shown that a bandgap can appear the spectrum of an epitaxial graphene bilayer. A number of problems in the thermodynamics of electrons in free and epitaxial graphene layers are considered as applications. Analytic expressions are obtained for the chemical potential and heat capacity in the limiting cases of low and high temperatures. Quantum oscillations of heat capacity in graphene are analyzed taking into account the Coulomb interaction. The Berry phase of epitaxial graphene is investigated.

The recent increase in the number of studies of RFe_11–xM_x compounds is related to their promising application as permanent magnets. However, the insufficiently high value of the Curie temperature T_C of these compounds is a barrier to their widespread use. The increase in the Curie temperature of these compounds is achieved by doping with the light nonmetallic atoms such as hydrogen, nitrogen, and carbon. In this paper, it is shown numerically that this doping leads to drastic changes of the electronic band dispersions in a wide energy region around the Fermi level. This in turn changes values of the magnetic moments of ions and Heisenberg exchange interaction parameters. The values of ab initio calculated magnetic moments and direct exchange interaction parameters make it possible to calculate the Curie temperatures for both parent and nitrogen-doped compounds within the mean-field approach to the Heisenberg model in the sample of YFe₁₁Mo, a typical representative of the R(Fe,M)₁₂L class. Theoretical values of T_C obtained for YFe₁₁Mo and YFe₁₁MoN (514 and 723 K respectively) are consistent with experimental ones (472 and 664 K) with an accuracy of 10%. Also, the calculated increase in T_C upon nitrogenization (about 200 K) is in good agreement with the experimental data.

The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.