Hole states in helium-like ions

Abstract

An analysis is made of the poles of the single-particle Green's function of helium-like ions in which electron correlation is taken into account on the basis of the model of singly filled orbitals. The energy of Hartree-Fock pole calculated through the use of the hydrogen-like wave functions for the orbitals turns out to be approximately equal to the exact value. The second pole, which corresponds to a different hole state, has a residue which vanishes as z increases and must be considered fortuitous.