The small-angle scattering structure functions of the single tetrahedron

Abstract

Basic properties of the SAS correlation function γ (r) and related functions are represented for a tetrahedron of edge length a. An interval splitting into four basic r-intervals in a sequence of cases for averaging the intersection volume between two tetrahedrons has been performed. Remarkably simple analytic expressions result in the first r-interval. Indeed, γ(r) is a polynomial of degree three. The coefficients are given explicitly. The asymptotic expansion I_\infty (h) is compared with the exact scattering intensity I(h).