Abstract
Based on first geometrical principles, the behaviour of the correlation function of Small-Angle Scattering of single, isolated particles is analyzed for the maximum distance of two points of the particle. This includes the observation of the second and third derivatives, which sensitively reflect the particle shape. The general, shape-independent analytical results are based on an approximation of the particle surface in the two extreme points using the main curvatures. The results are highly symmetrical simple square-root-expressions, which coincide with the limiting results of an ellipsoid. Singularities in the second derivative of the three-dimensional correlation function only occur in the special case in which all mean curvatures in the two intersection points of the maximum chord are exactly the same. This is the case with a single spherical particle.
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