A selfconsistent calculation of the rigid neutral atom density according to the auxiliary neutral atom model

TLDR: In this article, a selfconsistent numerical calculation of the displaced charge density n'(r) around a completely screened ionic potential V0 in a metal has been carried out for the Hartree-Fock-Slater equations.

Abstract: A selfconsistent calculation of the displaced charge density n'(r) around a completely screened ionic potential V0 in a metal has been carried out for the Hartree-Fock-Slater equations. V/sub /0 is the sum of the true ionic core potential Vion and the potential of a given (auxiliary) screening charge density nu (r). The resulting selfconsistent potential V'(r) is used to calculate the rigid neutral atom density n(r) which allows an approximate calculation of the metal selfconsistent potential. The main part of this work deals with the selfconsistent numerical calculation of the density n'(r) displaced by V0. The following approximations are made. The Kohn and Sham one-body formulation of the many-body problem is used. The wave equation is solved numerically inside a sphere of large but finite radius. The Coulomb potential due to the outer displaced charge is approximately calculated from the Friedel asymptotic formula. The continuous integration over the Fermi sea energy levels is replaced by a discrete summation. Selfconsistency is achieved by the use of a modified iterative process, using the linearized Thomas-Fermi equation in order to deal with the long range character of the Coulomb interaction. The method has been applied to metallic lithium and sodium, and results are given for n(r), on-the-Fermi-shell scattering matrix and nonstructural band structure properties.