A formula for relativistic atomic energies

Abstract

A formula is presented which expresses the relativistic energy of many-electron atoms and ions as a simple function of the configuration quantum numbers and of the nuclear charge Z. For systems containing only 1s, 2s, and 2p electrons, the formula involves a four by four matrix sigma (i mod j), whose sixteen elements are determined by thirteen theoretical Z-expansion coefficients and by three empirical parameters. The doublet splittings of 1s²2p ²P, 1s²2s²2P ²P, 1s²2p^{5 2}P and 1s²2s²2p^{5 2}P are treated, and the results compared with spin-orbit results and to first-order Z-expansion treatments. The accuracy of the formula is found to be comparable with that of the most accurate spin-orbit calculations. The effects of configuration mixing on the 1s²2s²2p ²P and 1s²2p⁵ 2P splittings are discussed in an appendix. Relativistic corrections to the ionization potentials of 1s²2s, 1s²2s², 1s²2s²2p and 1s²2s²2p⁶ are calculated.