Expectation values ofp1⋅p2as a measure of electron correlation in two-electron atoms

Abstract

We examine expectation values of ${\mathrm{p}}_1$⋅${\mathrm{p}}_2$ in ground states of He and ${\mathrm{H}}^{\mathrm{-}}$, the singly and doubly excited states of He, and the ground and low-lying valence states of the alkaline-earth-metal atoms. A simple commutator relation derived by Froese Fischer and Smentek-Mielczarek [J. Phys. B 16, 3479 (1983)] can be used to explain the sign and relative magnitudes of 〈${\mathrm{p}}_1$⋅${\mathrm{p}}_2$〉 in the ground states of He and ${\mathrm{H}}^{\mathrm{-}}$ and singly excited states of He. In the doubly excited states of He and in the ground and low-lying valence states of the alkaline-earth metals, the molecular model, which treats the electron–core-electron system as a floppy, linear triatomic ‘‘molecule,’’ correctly predicts signs and general trends for 〈${\mathrm{p}}_1$⋅${\mathrm{p}}_2$〉. These results represent an important test of the molecular model. The ability of this model to make intuitive predictions about quantities like 〈${\mathrm{p}}_1$⋅${\mathrm{p}}_2$〉 is a strong confirmation of its validity and utility.