Ground-State Wave Functions for He i andH−Obtained by the Superposition of Central Field Functions

Abstract

The ground-state wave functions of He i and ${\mathrm{H}}^{-}$ have been represented by the superposition of symmetrized analytic central field wave functions for the configurations $1s^2$, $1s2s$, $1s3s$, $2p^2$, $2p3p$, $3d^2$, and $4f^2$. The radial functions were taken to be the product of an exponential and a polynomial. The coefficients in the polynomials were chosen to insure the orthogonality of the one-electron wave functions. The parameters in the exponentials and the coefficients in the linear combinations of the wave functions for the different configurations were chosen so that the ground-state function gave the minimum energy. The resulting energies for He i and ${\mathrm{H}}^{-}$ are -5.79830 and -1.05190 respectively in units of the Rydberg for the corresponding atom. These results together with others are discussed.