The correlation function, intersect distribution and scattering from a cube

A calculation of γ(r), the correlation function which gives the X-ray scattering of a cubic object of uniform density, is given for the full range of r. A new method, which can be applied to other systems, is used. The function γ(r) and its first derivative are everywhere continuous, but γ′′(r) is discontinuous at r = L and r = L□2 (L = cube edge length). This leads to an intersect distribution of unexpected shape. The scattering intensity as a function of angle is calculated by Fourier inversion of γ(r).