The scattering of a scalar wave by a thin oblate body of revolution

The scattering of a scalar incident wave by a thin oblate body of revolution is studied. The scattering wave is represented as a distribution of ring singularities in a disk inside the body. Boundary conditions result in one-dimensional integral equations for singularity distributions. The asymptotic solution of these equations for thin bodies furnishes the singularity distribution as well as the radius α of the disk containing ring singularities. Example of the plane wave axially incident upon an oblate ellipsoid is presented. The total scattering cross-section is computed.