Nuclear spin relaxation by translational diffusion in solids. VIII. High-frequency limit for the simple hopping model

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Abstract
Nuclear spin relaxation rates due to magnetic dipole coupling between diffusing spins in a crystal are linear combinations of correlation functions J(p)( omega ). The high-frequency (low-temperature) form of these correlation functions is obtained for the simple hopping model by solving iteratively the rate equations for the occupancy probability functions describing the relative motion of a pair of spins on a lattice. The resulting high-frequency expansion of J(p)( omega ) is exact for all spin concentrations and gives higher-order terms beyond the familiar asymptotic limit. Numerical results are calculated for cubic lattices, two-dimensional hexagonal and square lattices and for the linear lattice.