Correlation Effects in Atoms. III. Four-Electron Systems

Abstract

The binding energy of the ground state of four-electron systems is investigated in the framework of Hartree-Fock perturbation theory. First, we show that the original problem can be decoupled into a series of helium-like equations describing pair correlation between electrons. Then, the variational-perturbation method is applied to each of these equations through fifth order in energy. We have obtained for the correlation energies the values ${E}_{\mathrm{corr}}(\mathrm{Be})=\ensuremath{-}0.0925$ atomic units (a.u.) and ${E}_{\mathrm{corr}}({\mathrm{B}}^{+})=\ensuremath{-}0.1096$ a.u. The experimental numbers are ${{E}_{\mathrm{corr}}}^{\mathrm{exp}}(\mathrm{Be})=\ensuremath{-}0.0944$ a.u. and ${{E}_{\mathrm{corr}}}^{\mathrm{exp}}({\mathrm{B}}^{+})=\ensuremath{-}0.1116$ a.u.