Correlated wavefunctions, energies, and one-electron radial densities for S states of the He atom

A priori approximation of integral-transform wavefunctions by Gauss quadrature provides an efficient and simple method for obtaining a finite approximation to the complete set of eigenfunctions of the Hamiltonian of a two-electron atom. These functions are described, and the energies and one-electron radial densities of the lower-lying S states of the He atom and the. ground state of H− are given. The energies are close to the exact values obtained from conventional variational results with Hylleraas-type functions extrapolated to the limit of an infinity of terms. The one-electron radial densities of the S states of He are found to have n −2 pseudonodes, where n is the principal quantum number, the triplet-state pseudonodes lying slightly closer to the origin than those of the corresponding singlet states.