The leading asymptotic term of the small-angle intensities scattered by some idealized systems

The leading asymptotic term of the small-angle scattered intensity contains oscillatory deviations from the well known Porod contribution when the sample interfaces are partly parallel to each other. The explicit expressions of these oscillatory contributions are evaluated for some cases which have practical relevance. The idealizations considered correspond to porous samples with a film coating the inner surfaces and to monodisperse samples made up of particles having a core of different density and a spherical, cylindrical or toroidal shape.