Correlation Effects in Atoms. III. Four-Electron Systems

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 $E_{\mathrm{corr}}\left(\mathrm{Be}\right)=-0.0925\mathrm{}$ atomic units (a.u.) and $E_{\mathrm{corr}}\left({\mathrm{B}}^{+}\right)=-0.1096\mathrm{}$ a.u. The experimental numbers are ${E_{\mathrm{corr}}}^{\exp }\left(\mathrm{Be}\right)=-0.0944\mathrm{}$ a.u. and ${E_{\mathrm{corr}}}^{\exp }\left({\mathrm{B}}^{+}\right)=-0.1116\mathrm{}$ a.u.