N.M.R. lineshapes for nuclei diffusing in magnetically heterogeneous systems

A theory for the N.M.R. lineshape of nuclei undergoing translational motion in a magnetically heterogeneous system is presented. The motion is modelled as a continuous diffusion process in a force field with a spatially varying diffusion coefficient. Closed-form analytical lineshape expressions are derived for several kinds of force field. The resulting lineshapes are compared with those predicted by the traditional discrete exchange model, which is based on a less realistic dynamical description. It is shown that the traditional approach can lead to a severely distorted picture of the microscopic behaviour of the system.