Form factor of any polyhedron: a general compact formula and its singularities

Abstract

A general and compact formula is established for the form factor of any polyhedron, which involves only the apex coordinates and the apex connections. For large diffusion vectorq, the form factor behaves likeq−3for generic directions, but it exhibitsq−2singularities in the directions perpendicular to the edges andq−1singularities in the directions normal to the faces. General results are established for these singularities. Using a Python implementation, illustrative examples are discussed. The generality of the formula and of its singularities are likely to be important for any discussion of scattering from polyhedral particles.