Co-spherical electronic configuration of the helium-like atomic systems

Abstract

The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius r, and angle θ characterizes their positions on sphere, are investigated. Unlike the previous studies, r is considered as a quantum mechanical variable but not a parameter. It is important that the “co-spherical” and the “collinear” configuration are coincident in two points. For θ=0 one obtains the state of the electron–electron coalescence, whereas the angle θ=π characterizes the e − n − e configuration when the electrons are located at the ends of the diameter of sphere with the nucleus at its center. The Pekeris-like method representing a fully three-body variational technique is used for the expedient calculations. Some interesting features of the expectation values representing the basic characteristics of the “co-spherical” electronic configuration are studied. The unusual properties of the expectation values of the operators associated with the kinetic and potential energy of the two-electron atom/ion possessing the “co-spherical” configuration are found. Refined formulas for calculations of the two-electron Fock expansion by the Green’s function approach are presented. The model wave functions of high accuracy describing the “co-spherical” electronic configuration are obtained. All results are illustrated in tables and figures.