Application of Wave Functions Containing Interelectron Coordinates. I. The Ground-State Energy of Lithium

Abstract

Several years ago, Pluvinage made a substantial advance in the use of interelectron coordinates in atomic systems by illustrating how the Schr\"odinger equation can be partially separated in such a way that the interelectron potential no longer appears as the perturbing term. His method gave excellent results when used to obtain variational energies of helium-like systems. In this paper, the Pluvinage method is modified in such a way that it can be applied with a reasonable amount of labor to more complex systems. In this modification, the nuclear coordinates act like Fermi-Dirac "particles" filling the energy levels pairwise, while the interelectron coordinates act like Bose "particles," all of which pile into the lowest energy continuum state. An accurate approximation technique is also developed for use in integrating functions containing three or more interelectron coordinates over the space of the nuclear coordinates. The modified Pluvinage approach is used in conjunction with the approximation technique to calculate the ground-state energy of neutral lithium. Internal evidence indicates that the approximation technique is better than 99% accurate in evaluating the individual integrals which appear. Although the wave function used here has no adjustable parameters, it yields an energy value for lithium which is slightly better than the two-parameter value of Wilson.