Longitudinal Spin Relaxation in SolidHe3

Calculations of the spin-lattice relaxation time, $T_1$, for ${\mathrm{He}}^3$ nuclei in solid ${\mathrm{He}}^3$ are made and the results are compared with experiment. A simple heuristic argument is first used which treats the two important relaxation mechanisms—diffusion and Zeeman-exchange coupling—as effectively independent and then a more precise calculation is made which takes into account interference effects. An expression for the exchange integral $J$ is obtained as a function of molar volume which, compared with the experiment, indicates an effective, reduced dipolar coupling. The effect of zero point motion on the dipolar interaction is investigated and using a very simple lattice model, it is found to be an important (but not necessarily the major) factor.