Nuclear Magnetic Relaxation by Hindered Rotations

The problem of the nuclear magnetic relaxation (NMR) due to hindered rotations in a crystal is treated considering the simple case of diatomic molecules assuming two antiparallel equilibrium orientations. An average time, ${\tau }_0$, during which the molecule oscillates around an equilibrium orientation, and a constant jumping time, ${\tau }_1$, are introduced. The spectral density is calculated as a function of ${\tau }_1$ and of $\tau ={\tau }_1+{\tau }_0$. For ${\tau }_1=0\mathrm{}$ the spectral density introduced by Bloembergen et al. is found if one assumes $\frac{\tau }{2}={\tau }_c$. For ${\tau }_1\ne 0$ and for $\omega \tau \mathrm{ll}1\mathrm{}$ the spectral density diminishes as ${\tau }_1$ increases. Correspondingly, the calculated $T_1\text{'}\mathrm{s}$ are, in general, longer than those calculated according to Bloembergen et al.