A perturbation treatment of the Hartree-Fock equations for 2s2p³P and¹P weakly quantized states of helium-like ions

The first-order Hartree-Fock (HF) equations for 2s2p 3P and 1P states of two-electron atomic systems are solved exactly. The solutions are used to evaluate the second-order HF energies exactly and the third-order HF energies with great accuracy. The zero and first-order terms in the expectation values of δ(γ), 1/γ, γ and γ 2 are also calculated for each orbital. The paper ends with a discussion describing the difficulties in using the variation and the variation perturbation methods for such highly excited states.