A relativistic single-particle potential for photoexcited electron orbitals of open-shell atoms

A single-particle potential for the calculation of relativistic photoexcited electron orbitals is introduced. Based upon the earlier work of Qian et al. (Phys. Rev. A 33, 1751 (1986)) and Boyle (Phys. Rev. A 48, 2860 (1993)) for non-relativistic electron orbitals, this relativistic potential is defined to include exactly all of the first-order electron correlations that appear in the diagrammatic perturbation series of the dipole polarizability and that contain potential corrections in the intermediate state. Analytic relationships associated with initial state jj-couplings are also considered. For example, among other things, the ability to rewrite the defined relativistic potential for a final state as an average term plus a correction to the defined average is investigated and presented.