Energy Eigenvalues, Eigenfunctions, and Transition Probabilities for a Paramagnetic Ion

The energy eigenvalues, eigenfunctions, and radiatively induced transition probabilities are computed perturbatively for an axially symmetric paramagnetic ion for arbitrary relative orientations of the crystal symmetry axis, static magnetic field, and time-varying magnetic field. Exact calculations are also reported for a system in which $S=\frac{1}{2}$, $I=\frac{1}{2}$. The bearing of these results on dynamic-nuclear-orientation experiments in paramagnetic samples is also discussed.