Perturbation-Theory Expansions Through 21st Order of the Nonrelativistic Energies of the Two-Electron Systems(2p)2 P3and(1s)2 S1

Abstract

The Hylleraas-Scherr-Knight variational perturbation method has been applied to the two-electron systems ${\mathrm{}\left(2p\right)\mathrm{}}^2 {}_{}{}^3{}_{}{}^{}P$ and ${\mathrm{}\left(1s\right)\mathrm{}}^2 {}_{}{}^1{}_{}{}^{}S$, carrying the calculations through to tenth-order perturbation wave functions. Various forms of expansions for the trial wave functions have been considered, e.g., the Hylleraas form and the Schwartz form, and numerical results are given in naturally spaced groups up to and including 252-term expansions. Estimates of the correct perturbation-energy coefficients through 21st order are tabulated, and the resulting nonrelativistic energies for $Z=2,3,\cdots ,10\mathrm{}$, are given with ten significant figures. To complete the tables the energies of the two states for ${\mathrm{H}}^{-}$ have also been calculated variationally, using the same expansions of trial wave functions as in the perturbation treatment, and for the ${\mathrm{}\left(2p\right)\mathrm{}}^2 {}_{}{}^3{}_{}{}^{}P$ state an extrapolated energy value of -0.2507097 measured in units of $Z^2\mathrm{Rh}$ has been obtained.