Analysis of SAS data dominated by multiple scattering

Beam broadening is discussed in the context of the standard formalism for multiple small-angle scattering, in which coherent single-particle scattering is incoherently, or stochastically, compounded by a random system of spherical particles in a uniform matrix. Bethe's analysis of scattering when sample thickness greatly exceeds the scattering mean free path is combined with the dynamical analysis of single-particle scattering to obtain a new scaling relation between the multiple-scattering intensity at arbitrary phase shift and the multiple-scattering intensity in the diffraction or small-phase-shift regime. A formula is derived for the curvature of the scattering at Q = 0 which expresses this scaling and which can be used in particle size determinations. It is shown that strong multiple scattering, as in very thick samples, tends to render beam broadening insensitive to the cross over from diffractive to refractive single-particle scattering.