Edge contributions to the Kirste–Porod formula: the truncated circular right cone case

The wide-angle correlation function γ(r) of a dilute system of particles, shaped as truncated circular right cones, is evaluated in closed form. The angular average of the contribution proportional to r3 gives γ′′′(0+), the value at the origin of the third derivative with respect to r of the corresponding small-angle correlation function. The value differs from that obtained by the Kirste–Porod formula by a negative contribution that arises from the two circular edges. Moreover, γ′′′(0+) turns out to be divergent in the case of circular right cones.