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 E₂₎ₑₑ (Be) =-0. 0925 atomic units (a. u. ) and E₂₎ₑₑ (B^+) =-0. 1096 a. u. The experimental numbers are {E₂₎ₑₑ}^exp (Be) =-0. 0944 a. u. and {E₂₎ₑₑ}^exp (B^+) =-0. 1116 a. u.