Anisotropic reorientation and non-exponential nuclear magnetic relaxation

The effect of interference or cross-correlation terms on the spin behaviour of a perturbed two-spin ½ system is analysed. The calculation, formulated within the semi-classical density matrix theory of relaxation, incorporates the necessary formalisms needed to treat anisotropic reorientation of the ‘bath’ molecules as well as motions characterized by a motional relaxation time slower than the inverse Larmor frequency. The physical consequence of the presence of finite cross-correlation terms is non-exponential decay and the magnitude of which is examined for various ratios of interaction constants, diffusional models, and internal geometries. The spin-rotation interaction, often the dominant relaxation mechanism for spin ½ nuclei, is considered in the light of its bearing upon the present problem. Also, general aspects of non-exponential relaxation as a result of interference effects are presented and discussed. It is concluded that marked anisotropic molecular reorientation generally has a negligible effect upon magnifying non-exponential decay, but that in isolated cases, internal geometry may be important.