Vol 80, No 2 (2017)

A systematic study of the ground-state properties of the entire chains of even–even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82, and 126 has been carried out using relativistic mean-field plus Bardeen–Cooper–Schrieffer approach. Our present investigation includes deformation, binding energy, two-proton separation energy, single-particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using nonrelativistic approach (Skyrme–Hartree–Fock method) along with available experimental data and indeed they are found with excellent agreement. In addition, the possible locations of the proton and neutron drip-lines, the (Z, N) values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail.

A practical model developed at the Joint Institute for Nuclear Research (JINR, Dubna) in order to describe the cascade gamma decay of neutron resonances makes it possible to determine simultaneously, from an approximation of the intensities of two-step cascades, parameters of nuclear level densities and partial widths with respect to the emission of nuclear-reaction products. The number of the phenomenological ideas used isminimized in themodel version considered in the present study. An analysis of new results confirms what was obtained earlier for the dependence of dynamics of the interaction of fermion and boson nuclear states on the nuclear shape. From the ratio of the level densities for excitations of the vibrational and quasiparticle types, it also follows that this interaction manifests itself in the region around the neutron binding energy and is probably different in nuclei that have different parities of nucleons.

The evolution of the reactor-antineutrino spectrum and the evolution of the spectrum of positrons from the inverse-beta-decay reaction in the course of reactor operation and after reactor shutdown are considered. The present-day status in determining the initial reactor-antineutrino spectrum on the basis of spectra of beta particles from mixtures of products originating from uranium and plutonium fission is described. A local rise of the experimental spectrum of reactor antineutrinos with respect to the expected spectrum is studied.

A multistage hybrid model intended for describing heavy-ion interactions in the energy region of the NICA collider under construction in Dubna is proposed. The model combines the initial, fast, interaction stage described by the model of hadron string dynamics (HSD) and the subsequent evolution that the expanding system formed at the first stage experiences at the second stage and which one treats on the basis of ideal hydrodynamics; after the completion of the second stage, the particles involved may still undergo rescattering (third interaction stage). The model admits three freeze-out scenarios: isochronous, isothermal, and isoenergetic. Generally, the HydHSD hybrid model developed in the present study provides fairly good agreement with available experimental data on proton rapidity spectra. It is shown that, within this hybrid model, the two-humped structure of proton rapidity distributions can be obtained either by increasing the freeze-out temperature and energy density or by more lately going over to the hydrodynamic stage. Although the proposed hybrid model reproduces rapidity spectra of protons, it is unable to describe rapidity distributions of pions, systematically underestimating their yield. It is necessary to refine the model by including viscosity effects at the hydrodynamic stage of evolution of the system and by considering in more detail the third interaction stage.

We develop a microscopic theory of a strong electromagnetic field interaction with gated bilayer graphene. Quantum kinetic equations for density matrix are obtained using a tight binding approach within second quantized Hamiltonian in an intense laser field. We show that adiabatically changing the gate potentials with time may produce (at resonant photon energy) a full inversion of the electron population with high density between valence and conduction bands. In the linear regime, excitonic absorption of an electromagnetic radiation in a graphene monolayer with opened energy gap is also studied.

Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

We show in details how to determine and identify the algebra g = {A_i} of the infinitesimal symmetry operators of the following pseudo-diffusion equation (PSDE) LQ ≡ \(\left[ {\frac{\partial }{{\partial t}} - \frac{1}{4}\left( {\frac{{{\partial ^2}}}{{\partial {x^2}}} - \frac{1}{{{t^2}}}\frac{{{\partial ^2}}}{{\partial {p^2}}}} \right)} \right]\)Q(x, p, t) = 0. This equation describes the behavior of the Q functions in the (x, p) phase space as a function of a squeeze parameter y, where t = e^2y. We illustrate how G_i(λ) ≡ exp[λA_i] can be used to obtain interesting solutions. We show that one of the symmetry generators, A₄, acts in the (x, p) plane like the Lorentz boost in (x, t) plane. We construct the Anti-de-Sitter algebra so(3, 2) from quadratic products of 4 of the A_i, which makes it the invariance algebra of the PSDE. We also discuss the unusual contraction of so(3, 1) to so(1, 1)∌ h². We show that the spherical Bessel functions I₀(z) and K₀(z) yield solutions of the PSDE, where z is scaling and “twist” invariant.

In the present paper we continue the project of systematic construction of invariant differential operators on the example of representations of the conformal algebra induced from the maximal cuspidal parabolic.

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability distribution of the total momentum of bodies system were obtained the partial differential equation of the second order. It is shown, that the equation for the probability distribution is solved jointly by classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents, transitions between asymptotic channels and, respectively for arising of quantum chaos.

The theory of neutrino oscillations rests on the assumption, that the interaction basis and the physical (mass) basis of neutrino states are different. Therefore neutrino is produced in a certain welldefined superposition of three mass eigenstates, which propagate separately and may be detected as a different superposition. This is called flavor oscillations. It is, however, not clear why neutrinos behave this way, i.e., what is the underlying mechanism which leads to the production of a superposition of physical states in a single reaction. In this paper we argue, that one of the reasons may be connected with the temporal structure of the process. In order to discuss the role of time in processes on the quantum level, we use a special formulation of the quantum mechanics, which is based on the projection time evolution. We arrive at the conclusion, that for short reaction times the formation of a superposition of states of similar masses is natural.

We show that the Calogero-type perturbation preserves the integrability and partial separation of variables for the Stark–Coulomb and two-center Coulomb problems, and present the explicit expressions of their constants of motion. We reveal that this perturbation preserves the spectra of initial systems, but leads to the change of degree of degeneracy.