Investigating one-dimensional diffusion by quasielastic neutron scattering: a theoretical approach

Scattering functions and full widths at half maximum for quasielastic neutron scattering (QENS) are calculated for diffusion in systems of one-dimensional channels. The self-correlation function for diffusion in isotropically oriented channels is given and it is found that this function diverges at the origin. The calculations are carried out for both normal and single-file diffusion and the influence of the ballistic phase is investigated. It is found that the ballistic phase influences the scattering functions very strongly for large diffusion coefficients. QENS data from the literature are analyzed with respect to this influence. The influence of three different resolution functions (triangular, Gaussian, and Lorentzian) is considered.