Comprehensive approach to motion-induced nuclear-dipole spin-lattice relaxation in the rotating reference frame

A comprehensive perturbation formalism is developed in order to relate the rotating-frame spin-lattice relaxation time $T_{1\rho }$ to the relative motions of the nuclear spins in a crystal lattice. A general relaxation equation valid in the entire temperature region is derived, from which both the strong-collision (so-called Slichter-Ailion theory) and weak-collision theory (valid in the motionally narrowed temperature region) are obtained as special cases. In the low-field transition region between the two theoretical approaches mentioned above, i.e., in the temperature region where the low-field $T_{1\rho }$ minimum occurs, the relaxation properties are not governed by internal motions alone (as it is true in the temperature region where the $T_{1\rho }$ minimum occurs in a high rotating field), but the spin dynamics associated with processes of internal equilibrization of the spin system play an important role. The results are illustrated by a random-walk mechanism of self-diffusion in cubic crystals.