Configuration-average energy shift owing to configuration interaction

A general expression for the shift in the average energy of an atomic electron configuration owing to configuration interaction is calculated in the second order of Rayleigh-Schrödinger perturbation theory, for arbitrary interacting configurations in either the relativistic (nlsj) or the nonrelativistic (nls) angular momentum classification scheme. This correction to the configuration-average energy is especially important for evaluating the effects of departures from pure j-j coupling when interpreting spectra from highly ionized atoms using the spin-orbit split array model. The total shift divides naturally into contributions from a set of distinct products of radial integrals, each multiply- ing the configuration average of a reducible four-body operator. For configurations that interact by single-electron excitation, n1l1j1 n2l2j2, the partial shift associated with each such product reduces to two terms, each proportional to a polynomial of degree 4 in the occupation numbers. The first & and is interpreted as a correction to the central potential. The second term contains the essential effects of configuration interaction, and vanishes unless the two spectator electrons (of the four-body operator) are equivalent. For two-electron excitations, only one term appears with no restrictions on the quantum numbers of the active electrons. Comparisons are presented with detailed level accounting results, and with experimental measurements.