Boundary-condition-determined wave function for the ground state of helium and isoelectronic ions.

Abstract

A simple nonvariational wave function for two electron atoms is described. The radial part is derived from the asymptotic one-electron wave functions that are modified to account for the proper core boundary conditions. The electron-electron correlation is described by an ansatz which has the correct behavior for ${\mathit{r}}_{12}$\ensuremath{\rightarrow}0 and ${\mathit{r}}_{12}$\ensuremath{\rightarrow}\ensuremath{\infty}. The additional parameter in this ansatz is calculated from a perturbation calculation. This wave function yields ground-state energies for the heliumlike atoms with Z=1 (${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$) to 10 (${\mathrm{Ne}}^{8+}$) within 0.0021--0.0068${\mathit{E}}_{\mathit{h}}$ of the exact energies, which is significantly better than obtained with previous models. We also calculated 〈${\mathit{r}}^{2\mathit{n}}$〉 and multipolar polarizabilities and performed other tests on this wave function. \textcopyright{} 1996 The American Physical Society.