Abstract
A recent $S$-matrix-based QED calculation of energy levels of the lithium isoelectronic sequence is extended to the general case of a valence electron outside an arbitrary filled core. Emphasis is placed on modifications of the lithiumlike formulas required because more than one core state is present, and an unusual feature of the two-photon exchange contribution involving autoionizing states is discussed. The method is illustrated with a calculation of the energy levels of sodiumlike ions, with results for $3{s}_{1/2}, 3{p}_{1/2}$, and $3{p}_{3/2}$ energies tabulated for the range $Z=30\char21{}100$. Comparison with experiment and other calculations is given, and prospects for extension of the method to ions with more complex electronic structure discussed.
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