Direct measurement of spin diffusion from spin relaxation times in solidHe3

We show that the spin-diffusion coefficient in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ may be obtained unambiguously from measurements of spin relaxation at low magnetic fields. For long times, the dipolar autocorrelation function decays as ${\mathit{t}}^{\mathrm{-}3/2}$. This follows purely as a consequence of the hydrodynamics of the system. From this we show that the low-frequency form of the dipolar spectral density function is J(ω)=J(0)-A${\mathrm{\omega }}^{1/2}$, where the constant A depends on the diffusion coefficient and is independent of the microscopic details of the system. Values of the spin-diffusion coefficient thus obtained are in good agreement with those obtained by conventional means. Moreover this method permits extension to higher densities and lower diffusion coefficients.