Small-Angle X-ray and Neutron Scattering of Polydisperse Systems: Determination of the Scattering-Particle-Size Distribution

In this paper, important questions related to the analysis of small-angle X-ray (SAXS) and neutron (SANS) scattering data produced by polydisperse systems are addressed. The calculation of the particle-size distribution [D(r)] is investigated through a gedanken experiment. A new recurrence numerical corrector method is presented. It is also compared to other methods normally used to calculate D(r): one based on Titchmarsh's transform and the other on Tikhonov's regularization technique. Some of their limitations as well as calculation and/or programming artifacts that may originate from their application are discussed. The results given by the new method give much better agreement with known solutions.