Time-domain farfield scattering of plane acoustic waves by a penetrable object in the born approximation

The low-contrast or (first-order) Born approximation is applied to the time-domain scattering of a plane acoustic wave by a penetrable object of bounded extent embedded in a homogeneous fluid. Closed-form analytic expressions are obtained for the spherical-wave farfield scattering amplitude related to homogeneous objects of the following shapes: an ellipsoid, an elliptic cone of finite height, an elliptic cylinder of finite height, and a tetrahedron. Relaxation effects are included. The results are, amongst others, useful as test cases for time-domain inverse-scattering algorithms.