Application of Wave Functions Containing Interelectron Coordinates. II. Approximate Energy Levels of Atoms

Abstract

This paper explores further the use of interelectron coordinates in constructing atomic wave functions. A simple method is developed for constructing wave functions of this type which yields surprisingly good values for the energy of a variety of atomic systems, in zero order. The Hamiltonian for the system is split into an unperturbed part, which is separable and which contains the interelectron potentials as well as the electron-nucleus potentials, and into a perturbing term which is always finite and which vanishes whenever an electron is far from the nucleus. The zero-order energies corresponding to this splitting of the Hamiltonian are at least an order of magnitude better for the light atoms than the energies given by the usual Thomas-Fermi theory, and are considerably better than the energies calculated with hydrogenic functions alone in first order.