Ground-State Wave Functions for He i and H^- Obtained by the Superposition of Central Field Functions

The ground-state wave functions of He i and H^- have been represented by the superposition of symmetrized analytic central field wave functions for the configurations 1s², 1s2s, 1s3s, 2p², 2p3p, 3d², and 4f². 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 H^- are -5.79830 and -1.05190 respectively in units of the Rydberg for the corresponding atom. These results together with others are discussed.