Ground-state energies for the helium isoelectronic series

Abstract

Variational calculations are reported for the ground state of the helium isoelectronic series. An ansatz is introduced and it achieves an accuracy comparable to that hitherto achieved only with basis functions containing logarithmic terms. Energies accurate to better than one part in ${10}^{14}$ are obtained for the ground states of He through ${\mathrm{Ne}}^{8+}$ using 308-term expansions, and the ground state of ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ using 455 terms.