Spin-Spin Interaction

Araki has suggested that spin-spin and spin-other-orbit interactions have an appreciable effect on the intervals of multiplets in spectra of heavy elements. He has shown that for a large number of elements the three intervals of a quartet (or the four of a quintet, etc.) can be calculated from a relation involving two arbitrary constants. We have calculated the matrix elements of spin-spin interaction for $d^n$ configurations, so that comparison can be made between different multiplets. The results are applied to 8 multiplets of Fe III, taking account of nondiagonal spin-orbit elements with second-order perturbation theory. The agreement obtained seems to warrant the conclusion that spin-spin effects are appreciable. An analysis of the electrostatic interaction in the $d^6$ configuration of Fe III has also been made.