SMALL-ANGLE MULTIPLE NEUTRON-SCATTERING IN FRACTAL MEDIA

Multiple small-angle neutron scattering from fractals is considered. It is shown that the; mean free path l in many cases is small compared to the commonly used sample thickness L. For multiple scattering when l much less than L the width of the intensity distribution q(L) is proportional to L(mu), where mu 1/(4 - D-s) and mu = 1/(D-v - 2) for the surface and volume fractals, respectively, and D-s,D-v is the corresponding dimensionality of the fractals. In both cases mu > 1/2 and the multiple scattering is a superdiffusion. The large-q tail of the intensity is the same as observed for single scattering. However, parts of the total intensity for q < q(L) and q > q(L) have the same order of magnitude and transition to the quasi-Guinier regime occurs at q much less than qL((Delta)) < xi(-1) where xi is cutoff for behaviour. It is shown that the failure of the diffusive random-walk description of the small-angle multiple scattering takes place in all cases when the mean square of the scattering angle theta(2) for the single scattering is an ill-defined quantity.