Solving the Schrödinger Equation for Helium-Like Ions with the Method of Configuration Weight Functions

Abstract

Schrödinger equations for helium-like ions from H⁻ to Ar¹⁶⁺ are solved by a novel method using the surfaces of the constant potential of electron-electron interaction. Similar to the method of configuration interaction, the wave function is represented as a linear combination of configuration wave functions, with the difference that their coefficients (referred to below as “configuration weight functions”), depend on the interaction potential. The basis functions are represented by the wave functions of noninteracting electrons in the Coulomb field of atomic nuclei. In the single-configuration approximation, the energies calculated for the ions appear to be lower than those calculated within the Hartree-Fock limit. The accuracy of energy calculations using three configurations (1s, 2s, and 3s functions) is close to the accuracy achieved with 35 configurations within the method of configuration interaction. The account of four configurations provides lower energies than those obtained by the configuration interaction method and slightly lower than those obtained with Hylleraas wave functions.