Nonlocal fluid density distribution in the vicinity of the critical point

The differential equation for the component local density of a binary fluid was obtained as a result of an isoperimetric problem of the system free energy minimization under condition of particle number stability. The obtained expression can be used in the calculation of liquid's profiles as well as in the investigation of thermodynamic properties in the vicinity of the critical point. An isoperimetric problem solution for the model binary fluid of the system free energy minimization under condition of particle number stability was obtained in different cases: fluid within flat parallel layer under a gravitational field, under a gravitational field and wall potential as well as under a wall potential for another equation of state.     

Transient energy density distribution of a rod under high-frequency excitation

Energy finite element analysis (EFEA) is an efficient way to solve high-frequency structural dynamics response problems. Up to now, EFEA has been used to deal with time-independent vibration problems. However, it is still necessary to understand the time dependent details of energy density distribution of a structure. To study the transient response of a rod under high-frequency sinusoidal excitation, the transient energy density governing equation for a rod is presented. The governing equation is solved, and the solution is verified using an analytical method. Example application to a rod is presented to illustrate the feasibility.     

Peninsulas of the neutron stability of nuclei in the vicinity of neutron magic numbers

On the basis of the Hartree-Fock method as implemented with Skyrme forces (Ska, SkM*, Sly4, and SkI2) and with allowance for an axial deformation and nucleon pairing in the Bardeen-Cooper-Schrieffer approximation, the properties of extremely neutron-rich even-even nuclei were calculated beyond the neutron drip line known earlier from theoretical calculations. It was shown that the chains of isotopes beyond the neutron drip line that contain N = 32, 58, 82, 126, and 184 neutrons form peninsulas of nuclei stable against the emission of one neutron and, in some cases, peninsulas of nuclei stable against the emission of two neutrons. The neutron- and proton-density distributions in nuclei forming stability peninsulas were found to be spherically symmetric. A mechanism via which the stability of nuclei might be restored beyond the neutron drip line was discussed. A comparison with the results of calculations by the Hartree-Fock-Bogolyubov method was performed for long chains of sulfur and gadolinium isotopes up to the neutron drip line.     

The peninsula of neutron nuclear stability in the vicinity of N = 258

The properties of extremely neutron-excessive nuclei with Z ?? 70, including the region of transuranium elements, are calculated beyond the previously theoretically known neutron drip line (NDL). The calculations are based on the Hartree-Fock approach using Skyrme forces (SkM*, SkI2, SLy4, Ska) with allowance for axial deformation and pairings in the BCS approximation. It is shown that the series of isotones with neutron number N = 258 outside of 2n NDL forms a peninsula of stable nuclei (PSN) with respect to the emission of one neutron. For SkM* forces, a PSN is formed by ³⁴⁴Rn, ³⁴⁶Ra, ³⁴⁸Th, and ³⁵⁰U nuclides.     

Spatial distribution of local density of states in vicinity of impurity on semiconductor surface

We present the results of detailed theoretical investigations of changes in local density of total electronic surface states in 2D anisotropic atomic semiconductor lattice in vicinity of impurity atom for a wide range of applied bias voltage. We have found that taking into account changes in density of continuous spectrum states leads to the formation of a downfall at the particular value of applied voltage when we are interested in the density of states above the impurity atom or even to a series of downfalls for the fixed value of the distance from the impurity. The behaviour of local density of states with increasing of the distance from impurity along the chain differs from behaviour in the direction perpendicular to the chain. The article is published in the original.     

Cold plasma dispersion relations in the vicinity of a Schwarzschild black hole horizon

We apply the ADM 3 + 1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It is concluded that negative phase velocity propagates in the rotating background whether the black hole is rotating or non-rotating.     

Equations of motion of a black hole in the quasistationary approximation

The motion of a black hole subject to external influences as observed by a distant observer is considered. Zerilli's equations are used to find the displacement of the black hole and the structure of the metric in the presence of other gravitating bodies. It is shown that in a region in which the curvature of space is small the contribution of the field of the accelerated black hole has the same form as the field of an ordinary body and that the motion of the black hole in the quasistationary approximation takes place in accordance with the laws of Newtonian dynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 22–26, November, 1980.We thank Professor K. A. Piragas for interest In the work and helpful discussions.     

Investigation of the properties of nuclei with extreme neutron excess in the vicinity of neutron magic numbers

Properties of even-even nuclei with extreme neutron excess in the vicinity of neutron magic numbers up to and beyond the neutron drip line (NDL) are calculated by the Hartree-Fock (HF) method using Skyrme forces (Ska, SkM*, Sly4, SkI2, SkP) with allowance for axial deformation and BCS-approximation pairing. It is shown that chains of isotones with the neutron numbers N = 32, 58, 82, 126, 184, and 258 beyond the NDL form peninsulas of nuclei stable with respect to emission of one neutron, and occasionally peninsulas of nuclei stable with respect to the emission of two neutrons. The length of these peninsulas in (N, Z) space depends on the choice of the Skyrme forces, while their locations are at the same N = 32, 58, 82, 126, 184, and 258 and do not depend on the choice of forces. The investigated isotones restore stability beyond the NDL due to the complete filling of subshells with high angular momentum and to the intrusion of corresponding neutron levels in the region of discrete bound states. The stability of the numerical solution to the HF equations for nuclei belonging to the peninsulas of stability is analyzed.     

Temperature distribution in a triangular laser rod

Variational methods are applied to give approximate solutions for the temperature distribution in a right equilateral triangular prism.     

Calculation of burnup of a black neutron absorber

The procedure of calculation of burnup of fuel and strong neutron absorber in a nuclear reactor is described. The method proposed here makes it possible to avoid difficulties associated with heterogeneous blocking of the absorption cross section. The effectiveness of the method is demonstrated by an example.     

Properties of lead isotopes in the vicinity of the neutron drip line

On the basis of the Hartree-Fock method with Skyrme forces of the Ska, SkM*, and Sly4 type, the position of the neutron drip line and the properties of neutron-rich lead isotopes are studied with allowance for deformations. It is shown that, in extremely neutron-rich nuclei, the neutron and proton density distributions are characterized by an anomalously large deformation parameter of β ～ 0.6. Also, nuclei of superdeformed lead isotopes have anomalously large root-mean-square radii. The existence of the isotopes ^266–288Pb, which are stable to the emission of one neutron, is predicted.     

On the Fermi approximation in slow neutron scattering

In this paper a general connection between the scattering from a bound and a free nucleus is derived in terms of formal scattering theory. The basic idea is to eliminate the interaction Hamiltonian between neutron and nucleus. Then theT-operator for a bound nucleus can be expressed by that of the free nucleus and its binding potential. From this equation an expansion is given as a power series in the binding potential for the nucleus. For slow neutron scattering the first term of the series leads to Fermi's approximation. The second term is the first correction to Fermi's approximation which contains no divergences for point scatterers contrarily to theories of other authors. In particular the correction to Fermi's approximation of the scattering amplitude is calculated for an elastically bound proton in the limit of zero-energy neutron.     

Systematic for parity distribution in nuclear level density near neutron separation energies

The correct form of nuclear level density function ρ(U,J,π)$\rho (U,J,\pi )$ is required to calculate nuclear cross-sections needed for various applications ranging from reactor designing, nuclear astrophysics, etc., to transmutation of nuclear waste. The asymmetrical statistical distribution of parity of nuclear levels at low energies poses an intriguing problem leading to larger uncertainties in the calculated values of cross-sections. On the basis of high resolution data available on individual resonance parameters (Eo,Jπ,Γn)$(E_o,J^{\pi },{\Gamma }_n)$ for s- and p-wave neutrons, mass and energy dependence formulae for the parity distribution in the nuclear level density have been proposed which supports the fact of equipartition of parities at high excitation energies.     

The measurements of thermal neutron flux distribution in a paraffin phantom

The term ‘thermal flux’ implies a Maxwellian distribution of velocity and energy corresponding to the most probable velocity of 2200 m s^???1 at 293.4 K. In order to measure the thermal neutron flux density, the foil activation method was used. Thermal neutron flux determination in paraffin phantom by counting the emitted rays of indium foils with two different detectors (Geiger–Muller counter and NaI(Tl)) was the aim of this project. The relative differences of the outcome of the experiments were between 2.5% and 5%. The final results were compared with MCNP4C outputs and the best agreement was generated using NaI(Tl) by a minimum discrepancy of about 0.6% for the foil placed 8.5 cm from the neutron source.