Atomic fine-structure inversions explained as first-order relativistic corrections to the Hartree-Fock energy

Abstract

It is shown that the fine-structure inversions in highly excited d and f levels of atoms containing a single valence electron can be explained solely as first-order relativistic corrections to the energies of the non-relativistic Hartree-Fock wavefunctions. The variation (with respect to the position of the atom in the periodic table) of the contribution Delta EK arising from the relativistic correction to the core exchange potential, shown to be responsible for the inversions, is related to changes in the differential overlaps between the valence and the outermost core orbitals and their first-order relativistic corrections. It is further shown that although the magnitude of Delta EK decreases less rapidly with the principal quantum number n of the valence electron than 1/n3 for intermediate values of n, it varies as 1/n3 in the limit of large n.