Theory of Hyperfine Structure

Abstract

Considering the classical electric and magnetic interactions between atomic electrons and the nucleus, we arrive at a representation of the hyperfine interactions in terms of a multipole expansion of the field potentials. Treating these noncentral interactions in first order perturbation theory we can give the form of the general interval structure and analyze for the multipole interaction constants using Racah coefficients. Pertinent matrix elements for a single valence electron are calculated relativistically. Some second order terms of the dipole and quadrupole interactions are calculated as they affect the interpretation of the first order octupole interaction. In this work we also take into account quantitatively the effect of some electronic configuration interaction. Finally the values of nuclear magnetic octupole moments expected according to different models are calculated and compared with the experimental data thus far collected. Generally the measured octupole moments are in as good agreement with the values predicted by the single-particle shell model as are the corresponding dipole moments.