Calculation of Second-OrdergShifts of Paramagnetic Ions in Crystals

A formula is derived for the second-order spin-orbit coupling correction to the $g$ value of a paramagnetic ion. The case considered is that of an ion whose orbital moment is quenched by the electrostatic field of an ionic-crystal host so that an orbitally nondegenerate spin multiplet forms the ground state. The results are applied to the case of ${\mathrm{Ni}}^{+}$ in LiF and NaF.