Nuclear Relaxation in Solids due to Molecular Rotation at Low Temperatures

A quantum‐mechanical treatment of nuclear spin–lattice relaxation due to molecular rotation in the solid is presented. It is shown that at low temperatures, where this treatment is valid, the rate of relaxation is directly proportional to the rates of transitions among the torsional levels and to the extent to which those transitions alter the expectation value of the diple–dipole Hamiltonian. The form of the expression for $T_1$ is analogous to the usual form obtained by a correlation function approach, in the limit ${\omega }_0{\tau }_c\text{\hspace{0.17em}≫\hspace{0.17em}1}$ , if the inverse of the correlation time is identified with an appropriate average transition rate among torsional levels. It is predicted that at very low temperatures the apparent activation energy of the correlation time should be much smaller than the height of the barrier to rotation.