Approximate Analytical Wave Functions for the 1sns 1S States of He and He-Like Ions

Calculations have been made for the 1s2s, 1s3s, and 1s4s 1S states of He and He-like ions, assuming wave functions of the symmetrized product form, u(1) v(2)+u(2) v(1). The results are the best obtained till now using such a functional form, and are even better than some recent calculations which, in addition, use angular correlations. The energy values obtained for He are: 2.14307, 2.06036, and 2.03320 for the 1s2s, 1s3s, and 1s4s 1S states, respectively. The wave functions obtained were checked by other criteria besides the energy criterion.