Research Report No. EM-126 Higher Order Approximations in Multiple Scattering Ⅰ. Two-Dimensional Scalar Case Ⅱ. Three-Dimensional Scalar Case

摘要

I. 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 obyersation. Interaction terms of degrees d-1/2, d-1, and d-3/2 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.nThe method of I is extended to cover the three dimensional scalar problem for two bodies of arbitrary shape. All interaction terms of order d-1 and d-2 are given.