Variational Perturbation Theory Study of Some Excited States of Two-Electron Atoms

The Hylleraas–Scherr–Knight variational perturbation method has been applied to the two‐electron states ${\text{1s3s}}^{\text{3,1}}S$ and ${\text{1s3p}}^{\text{3,1}}P$ . The calculations have been carried through to 20th‐order wavefunctions, with 96‐, 126‐, and 162‐term expansions of the Hylleraas type, thus yielding estimates of the energy through the 41st order. The perturbation energy coefficients are tabulated through the 21st order for the states ${\text{1s2s}}^{\text{3,1}}{\text{S, 1s2p}}^{\text{3,1}}{\text{P, 1s3s}}^{\text{3,1}}S$ , and ${\text{1s3p}}^{\text{3,1}}P$ , and the corresponding nonrelativistic energies are presented for the first 10 elements of the helium isoelectronic sequence, with the exception of H⁻ to which the perturbation expansions do not apply. Where comparison is possible, our results are in fair agreement with those obtained from conventional variational calculations. A survey of the variational perturbation procedure is also given, presenting the basic formulas and phrasing two important theorems.