Analytical formulation improves multiple scattering calculations for spherical particles, suggesting enhanced precision in ultra-small-angle neutron and X-ray scattering methods.
We start from an analytical formulation for the coherent multiple scattering treatment – similar to Mie scattering – for spherical particles. Then, we revisit the Born approximation with an approximation for all higher-order terms. Finally, we draw conclusions from those calculations and formulate an approximative model to describe ultra-small-angle neutron scattering and ultra-small-angle X-ray scattering data. In all calculations, we can specify the conditions for coherent multiple scattering. Several examples are provided to show the quality of the simple approximation in comparison with exact calculations and experiments.
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Frielinghaus et al. (2025) studied this question.
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