The diffusive behavior of particles can be studied with the help of quasielastic light or neutron scattering. Diffusion within a fractal space does not follow the normal law 〈${\mathit{r}}^2$〉∼t, r being the displacement in time t. In this paper we study quasielastic scattering in fractal spaces and try to predict new features which may be observed experimentally. Examples of such systems may be the AgI percolation clusters in glassy AgI borate and phosphate superionic conductors, gel-type protonic conductors, and biological systems. For such fractal systems our calculated line shape of scattered intensity, S(k,ω), is found to be oscillatory in nature unlike the Lorentzian centered at ω=0, for normal diffusion. The maximum scattered intensity S(k,0) has a power-law dependence on k. Also the half width at half maximum is found to be independent of k.

• Received 6 June 1995

DOI:https://doi.org/10.1103/PhysRevB.52.10021