A perturbation treatment of the Hartree-Fock equations for 1s2p 3P and 1P states of helium-like ions

Abstract

The first-order Hartree-Fock equations for the 1s2p 3P and 1P states of two-electron atomic systems are solved exactly. The solutions are used to evaluate the second-order Hartree-Fock energies exactly and the third-order Hartree-Fock energies with great accuracy. New and more accurate expressions for the correlation energies of these states are given. The zero- and first-order terms in the expectation values of δ(r), 1/r, r and r2 are also calculated for each orbital. Outlines of the methods involved in the solution of the first-order Hartree-Fock equation for any orbital and in the evaluation of integrals occurring in the second- and third-order energies are given in a series of mathematical appendixes at the end of the paper.