Molecular motion in anisotropic medium. I. The effect of the dipolar interaction on nuclear spin relaxation

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Abstract
The diffusion equation in the presence of a restoring potential is solved and the result is applied to dipolar NMR relaxation in liquid crystal solvents. The potential imparted by the solvent is approximated by a series of rotation matrices of rank two. The solution of the diffusion equation is expressed as an infinite series of rotation matrices. It is then shown that only the terms of rank two of this series are necessary to compute the dipolar spectral densities. This theory predicts the spectral densities to be different for different z-projection numbers, even in the case of extreme narrowing.