A simple model for the influence of motion on the NMR line shape

A problem as old as NMR is that of the influence of motion on the shape of the NMR absorption signal, or equivalently the shape of the FID. Although it is known that motion means narrowing, only two limiting cases are well defined. In the rigid solid, one has a clean theoretical expression for the FID function, in terms of the secular part 3TSS of the spin-spin interactions, most of the time essentially dipolar (1). This is insufficient to know the FID shape, nor that of its Fourier transform, the absorption f signal, but one can compute the first few moments of the latter and obtain reasonably good value for its frequency width Ad)0 (1-3). The other extreme is that of a fast motion whereby the spin-spin interactions have a vanishing average value and are modulated at a rate x' which is fast on the time scale of the solid-state FID decay rate