Correlation Energy in the Ground State of He I

Abstract

With a view of examining the effects of configuration interaction in a simple case, the three term and six term expressions given by Hylleraas for the ground-state wave function of He I have been expanded in series of Legendre functions of the cosine of the angle between the two radius vectors. The coefficients in these expansions are functions of $r_1$ and $r_2$, the distances of the two electrons from the nucleus. The various component functions are presented, together with the coefficients with which these functions enter the expansions, and their contributions to the total energy. A discussion is given of the method of estimating the magnitude of the correlation, or configuration interaction, energy. Evidence is presented that the total correlation energy is at least $-0.129\mathrm{}{R}_{\mathrm{He}}\mathrm{hc}$ and may be even more negative. Of this amount it is estimated that $-0.056\mathrm{}{R}_{\mathrm{He}}\mathrm{hc}$ is associated with the radial part of the correlation energy, $-0.075\mathrm{}{R}_{\mathrm{He}}\mathrm{hc}$ with the angular part, and $+0.002\mathrm{}{R}_{\mathrm{He}}\mathrm{hc}$ with the mixed part.