Effective operators in the atomic hyperfine interaction

TLDR: In this article, the many-body perturbation theory (MBPT) is applied to the atomic hyperfine interaction and the results are interpreted in terms of effective operators for systems with a single valence electron such as the alkali atoms.

Abstract: The many-body perturbation theory (MBPT) is reviewed and applied to the atomic hyperfine interaction. Graphical methods are introduced by without mathematical details. The results are interpreted in terms of effective operators. For systems with a single valence electron-such as the alkali atoms-this operator has the same form as the ordinary hyperfine operator and is identical to the operator commonly used in the analysis of experimental hyperfine data. The origin of different contributions to this operator is discussed. Numerical results are given for the 22S and 22P states of the lithium atom, where accurate MBPT calculations have recently been performed. For systems with several valence electrons additional parameters are needed or, alternatively, the parameters of the one-body effective operator are allowed to be term-dependent. Recent experiments and corresponding theoretical investigations on alkaline-earth elements, with two valence electrons, are reviewed and, in particular, MBPT calculations on the calcium atom are discussed.