Intersect distributions and small-angle X-ray scattering theory. III. The intersect distribution for an ellipsoid

An expression is developed for the intersect distribution function G(M) for an ellipsoid. The intersect distribution is useful for studying how the intensity of small-angle X-ray scattering is affected by the shape of the scattering particles in suspensions of identical, independent, randomly oriented particles when both the particles and the solvent have constant electron densities. The expression for G(M) for an ellipsoid can be employed in numerical calculations of the scattered intensity. In addition, the techniques and concepts developed to obtain G(M) for an ellipsoid can be useful in finding this function for other particles less symmetrical than a sphere or a solid of revolution.