Scattering of light and neutrons in a model for superionic conductors

We discuss the cross sections for neutron scattering and light scattering from a superionic conductor. The motion of the mobile ions is treated as an independent continuous diffusion process through a periodic potential. While this determines the neutron scattering intensity completely, the light scattering is, in addition, strongly influenced by the spatial variation of the polarizability. This leads to selection rules and to differences between the two kinds of spectra. We present a rather complete study of a one-dimensional model which displays the general features of the problem. The results are based on a numerically accurate solution of the corresponding Fokker-Planck equation.