Some calculations on the ground and lowest-triplet state of the helium isoelectronic sequence with the nucleus in motion.

Abstract

The method described in the preceding paper for the solution of two-electron atoms, which was used to calculate the 1 $^{1}$S and 2 $^{3}$S states of helium and heliumlike atoms within the fixed-nucleus approximation, has been applied to the case where all three particles are in relative motion. The solutions in the present case automatically include the effects of the mass polarization term and are compared with the results obtained for the term by using first-order perturbation theory with the fixed-nucleus wave functions. The input data for a particular atom consist of the atomic number, as before, but now the corresponding mass of the nucleus must be given also. Nonrelativistic energies with the nuclear mass included in the calculation have been obtained for the 1 $^{1}$S and 2 $^{3}$S states for Z ranging from 1 to 10. The energy with the nucleus in motion can be expressed only to eight significant figures (SF's) given the accuracy with which the relevant physical constants are known at present. All the results given here are computed as if these constants were known to ten SF's so that errors not incurred due to rounding. Convergence of the energies to ten SF's for both the singlet and triplet state was reached with a matrix of size 444 for Z values from 2 to 10. Convergence for the ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ ion was a little slower.