Superposition of Configurations in the Ground State of He I

Abstract

To obtain some understanding of the role played by various configurations in configuration interaction, the Hylleraas six-term expression for the ground-state wave function of He I has been expanded in series of orthogonal functions. To determine the degree of dependence of the coefficients of the expansion on the specific function used for the ground state, the Hylleraas three-term expression was also expanded. Two sets of orthogonal functions were used. One set consisted of orthogonalized symmetrized product type wave functions where the functions for the individual electrons were found from a Hartree self-consistent field without exchange. The second set consisted of orthogonalized variationally determined analytic wave functions. The results emphasize the large number of configurations which would have to be considered if the Hylleraas wave function were to be represented with high accuracy. After $1{s}^{2}$ the largest contributors among the configurations considered were $2{p}^{2}$ and $2{s}^{2}$.