First-Order Perturbation Corrections to the Hartree-Fock Approximation for Helium

Abstract

Variational perturbation theory has been used to compute the first-order wave function for the ground state of the helium atom, in a scheme where the Hartree-Fock function is treated as the zeroth-order approximation. The first-order function was approximated by a Hylleraas-like expansion, explicitly containing $r_{12}$. We obtain a total energy through third order of -2.90262 a.u., as compared with the nonrelativistic eigen-value of -2.90372. The first-order corrections to expectation values of a selection of one- and two-electron operators have been computed. The calculations have also been done for the isoelectronic ions, ${\mathrm{H}}^{-}$, ${\mathrm{Li}}^{+}$, and ${\mathrm{Be}}^{2+}$.