Chord length distribution density and small-angle scattering correlation function of the right circular cone

From geometric considerations, correlation functions for the right circular cone and their second derivatives are calculated and represented by a. sum of five parametric integrals at most. For this, four main types of cones are distinguished, which make possible a systematic consideration of interval splitting at all. The correlation function and the distribution density of the chord length for isotropic uniform random chords are all continuous functions if the limiting cases, i.e., circle and rod, are excluded. The actual parameters radius and hei(:ht of the cones sensitively influence the behaviour of the chord length distribution density. The behaviour of the functions is characteristic of cones exclusively and does not agree with any of the geometrical figures investigated by now. (C) 1999 Elsevier Science Ltd. All rights reserved.