Z-1/2expansion of the unrestricted Hartree-Fock equations for the (1s)(1s )1S states of helium and helium-like ions

Abstract

An equation is derived for the first of the half-order terms, u1/2, in the Z-1/2 expansion of the orbital wave functions for the (1s)(1ś) 1S ground state of helium and helium-like ions This equation is solved by expanding u1/2 in a series of generalized Laguerre polynomials, and two cases are considered, in which 12 and 30 terms respectively are taken in the series. The effect of u1/2 on the second- and third-order energy coefficients E2 and E3 is next studied. It is shown that the inclusion of u1/2 accounts for 92% of the Z-independent term in the series expansion of the radial correlation energy, and that considerable improvement is made on the restricted Hartree-Fock value of E3.