Scaling of the dynamic structure factor of an adsorbate on a fractal surface

The possibility is suggested that quasi-elastic neutron scattering measurements can yield the spectral dimension characteristic of diffusion on a fractal surface. A scaling relation is derived which connects where is the fractal dimension, to the momentum and frequency dependences of the incoherent structure factor. An explicit theory of the line shape, non-Lorentzian in general, is given for the case of singly connected fractals. Experimental feasibility is indicated on the basis of approximate arguments. A brief discussion of measuring the adsorbate's coherent static structure factor by contrasting coherent elastic scattering is given.