2021/06/21 by Evgeny Z. Liverts, Liverts, Evgeny Z.
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Atomic Physics (physics.atom-ph) #Atomic and Molecular Physics #FOS: Physical sciences
paper · pdf · doi:10.48550/arxiv.2106.11254
openalex publication_date 2021/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 "electrons-on-sphere" 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 characteristic of the "electrons-on-sphere" 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 "electrons-on-sphere" configuration are found. Refined formulas for calculations of the two-electron Fock expansion by the Green's function approach are presented. The analytic wave functions of high accuracy describing the "electrons-on-sphere" configuration are obtained. All results are illustrated in tables and figures.