A theory for the evaluation of small-angle scattering diagrams of quasi radially symmetric particles considering polydispersity and deviations from radial symmetry

A general theory has been developed describing the scattering intensity of a polydisperse dilute ensemble of particles. These particles are assumed to be mainly radially symmetric. Deviations from radial symmetry are treated quantitatively using an expansion of the electron density in terms of multipole components. The particle radii are assumed to have a Gaussian-like distribution. The electron density of the particle core is allowed to be different from that of the solvent. As a practical application of this theory a Fortran 77 program was written which determines the radial electron density profile, the standard deviation of the radii, and additional parameters describing the deviations from spherical symmetry directly from the measured intensity.