Neutron incoherent scattering law for diffusion in a potential of spherical symmetry: general formalism and application to diffusion inside a sphere

A general formalism is presented to calculate the neutron incoherent scattering law for diffusion in a potential of spherical symmetry and applied to the problem of diffusion of a particle in the interior of a sphere with an impermeable surface. The shape of the spectra and their behaviour versus the momentum transfer predicted by this model is discussed and compared to those of simpler models. This model should satisfactorily describe molecular diffusion in restricted geometries in three dimensions, e.g. water molecules around hydrophilic centres in solids.