Field Dependence of the Direct-Process Spin-Lattice Relaxation Time in Rare-Earth Salts

The field dependence of the direct-process spin-lattice relaxation time for rare-earth salts having $g_{\perp }=0\mathrm{}$ is computed taking into account dipolar coupling between the spins. Comparison is made with the corresponding relaxation time calculated in a modified effective-field approximation, and the presence of terms not found in the modified effective-field formula is noted. Conditions that must obtain for the effective-field approximation to be valid are discussed, and a numerical evaluation of the relaxation time for dysprosium ethyl sulfate is given. Extension of the calculation to salts not having $g_{\perp }=0\mathrm{}$ is also considered.