Perturbation Treatment of the Hartree-Fock Equations for2p2D1andP3Weakly Quantized States of Helium-like Ions

Abstract

The first-order Hartree-Fock (HF) equations for the $2{p}^{2}^{1}D$ and $^{3}P$ 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 $\frac{1}{r}$, $r$, and ${r}^{2}$ are calculated for the $2p$ orbital in each case. The results of this paper for the $2{p}^{2}^{1}D$ state of the helium atom are compared with those of experiment and another calculation.