Higher-Order Approximations in Multiple Scattering. I. Two-Dimensional Scalar Case

Abstract

A formula is derived which expresses the perturbed scattering amplitudes of a combination of two arbitrary cylinders as a function of the unperturbed scattering amplitudes of the individual cylinders. The formula is valid when the spacing of the scatterers is large compared to their dimensions. It involves derivatives of the scattering amplitudes with respect to the angles of incidence and of observation. Interaction terms of degrees d−½, d−1, and d−½ are taken into account, where d is the spacing. Verification is obtained in a special case. The result is employed to calculate the total scattering cross section.