The Ground State Energy of Heavy Atoms According to Brown and Ravenhall: Absence of Relativistic Effects in Leading Order

It is shown that the ground state energy of heavy atoms is, to leading order, given by the non-relativistic Thomas-Fermi energy. The proof is based on the relativistic Hamiltonian of Brown and Ravenhall which is derived from quantum electrodynamics yielding energy levels correctly up to order $\alpha^2$Ry

La soviétisation culturelle de la Bessarabie: le cas de l'Union des écrivains moldaves à l'époque stalinienne

This article aims at tracing a model of cultural Sovietization of the territories incorporated by the USSR in 1940, based on the study of this process in Bessarabia, a former Romanian province which became in June 1940 a Soviet republic (the Moldavian Soviet Socialist Republic - MSSR) and more specifically on the case of the Moldovan Writers' Union. The history of this process dates back to the creation in 1924 on a small territory on the left bank of the Dniester of the Moldavian Autonomous Soviet Socialist Republic (MASSR) within the Ukrainian Soviet Socialist Republic. The author will therefore try to pursue the rather discontinuous and contradictory development of the creation of a cultural policy in the center of the Soviet Empire and implemented in a small Western Soviet republic, but no less important given its strategic position. This cultural policy is elaborated and applied in a tacit or explicit relationship of convergence or divergence with other integration models applied in other regions annexed in the same period (1940-1944), in an effort to consider local and regional specificities

Thomas-Fermi Calculation of the Interlayer Force in Graphite

A model of a graphite crystal is proposed in which planar layers of positive charge are considered instead of the point charges of nuclei. The interlayer electronic density is calculated integrating both the Thomas-Fermi and the Thomas-Fermi-Dirac equations. From these densities, the total energy of the electrons is calculated including corrections for inhomogeneity in the form of Weizsäcker and Kirzhnits. The influence of the different corrections is studied with the result that the best method is to calculate the density from the Thomas-Fermi-Dirac equation and to take into account the inhomogeneity corrections in the form of Kirzhnits

Self-consistent solution of Kohn-Sham equations for infinitely extended systems with inhomogeneous electron gas

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves iterations with alternate solving of the Poisson and Schr\"{o}dinger equations. One of problems of such an approach is that the charge distribution renewed by means of the Schr\"{o}dinger equation solution does not conform to boundary conditions of Poisson equation for Coulomb potential. The resulting instability or even divergence of iterations manifests itself most appreciably in the case of infinitely extended systems. The published attempts to deal with this problem are reduced in fact to abandoning the original iterative method and replacing it with some approximate calculation scheme, which is usually semi-empirical and does not permit to evaluate the extent of deviation from the exact solution. In this work, we realize the iterative scheme of solving the Kohn-Sham equations for extended systems with inhomogeneous electron gas, which is based on eliminating the long-range character of Coulomb interaction as the cause of tight coupling between charge distribution and boundary conditions. The suggested algorithm is employed to calculate energy spectrum, self-consistent potential, and electrostatic capacitance of the semi-infinite degenerate electron gas bounded by infinitely high barrier, as well as the work function and surface energy of simple metals in the jellium model. The difference between self-consistent Hartree solutions and those taking into account the exchange-correlation interaction is analyzed. The case study of the metal-semiconductor tunnel contact shows this method being applied to an infinitely extended system where the steady-state current can flow.Comment: 38 pages, 9 figures, to be published in ZhETF (J. Exp. Theor. Phys.

Study of interplanar binding in graphite by extended Thomas-Fermi theory

A model of a graphite crystal is used which consists of a set of parallel slabs of positive charge immersed in an electron sea. Each slab, about 1 Å wide, contains the charge of the nucleus and five electrons per carbon atom, homogeneously distributed in the volume of the slabs. The electron density in the region between slabs is calculated from Thomas-Fermi-Dirac theory including corrections for inhomogeneity to the kinetic energy and correlation energy. Also, a calculation is reported with the electron density obtained by a minimization of the Thomas-Fermi-Dirac-Kirzhnits functional. The results are in semiquantitative agreement with empirical data