Spin-Lattice Relaxation Time of Samarium Ethyl Sulfate

The spin-lattice relaxation time $T_1$ of ${\mathrm{Sm}}^{3+}$ in the ethyl sulfate is computed. It is shown that $T_1$ in the direct-process region should exhibit a large anisotropy with respect to the direction of the external magnetic field. The necessary Zeeman admixture of excited levels into the ground level is shown to be much smaller when the external field is parallel rather than perpendicular to the symmetry axis. This is because, on the one hand, the levels connected by a parallel field lie in the next $J$ multiplet, some 1100 ${\mathrm{cm}}^{-1\mathrm{}}$ away. On the other hand, a perpendicular field can connect the ground state with a level within the ground multiplet, only 53.6 ${\mathrm{cm}}^{-1\mathrm{}}$ away. This is shown to be a general result for ions with small $J$ values in crystals of moderately high symmetry.