Hyperfine fields, spin orbit coupling, and nuclear magnetic moments of rare-earth ions

An investigation is presented of the related problems of hyperfine fields, spin orbit coupling, and the determination of nuclear magnetic moments, all of which are strongly dependent on the 4f charge distributions in the rare earths and play an important role in Mössbauer, NMR, paramagnetic resonance, and optical absorption measurements. The discussion is based on a set of conventional approximate nonrelativistic Hartree-Fock wave functions which were determined for nine ions of the series. Results are presented, and the various approximations and assumed relationships between these quantities (listed in the title) are discussed in the light of comparisons between theoretical predictions and experiment.