The small-angle scattering correlation function of two infinitely long parallel circular cylinders

The correlation function γ(r,d,s) of a pair {A,B} of infinitely long parallel circular cylinders of diameter d, the centers of which are separated by a distance s, is investigated. Based on first principles, two basic constellations (widely separated cylinders and close cylinders) are analyzed. Integral representations were obtained, applications of which are in the field of the interpretation of scattering experiments of the so-called controlled porous glasses (nearly cylindrical macropores in the region of 100 nm) and of pattern recognition of geometric figures. Series expansions of γ(r) at r=0 and the behavior of γ″(r) are analyzed for the special case s=d.