Nuclear spin relaxation by translational diffusion in liquids and solids: high- and low-frequency limits

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Abstract
Nuclear spin relaxation rates due to magnetic dipole coupling between spins of a single species undergoing relative diffusion depend on two-spin correlation functions J(p)( omega ). The high- and low-frequency limits of J(p)( omega ) are discussed for liquids, cubic crystals and two- and one-dimensional systems. It is shown that the low-frequency form of J(p) ( omega ) is J(p)(0)-A3 omega 1/2 in liquids and crystals, A2ln omega -1 in two-dimensional systems and A1 omega -1/2 in one-dimensional systems and expressions for the coefficients A1, A2 and A3 are derived which are valid for any diffusive model whose long-range, long-time behaviour may be described by the diffusion equation. The high-frequency form of J(p)( omega ) is derived for a simple-hopping model of spins on one-, two- and three-dimensional lattices and in each case J(p)( omega ) is of the form B omega -2. Expressions are derived for the coefficient B, for each dimension, which correctly include the effect of correlations between the hops of the spins.