On the Capacity and Rayleigh Scattering for a Class of Non-Convex Bodies

Exact expressions are obtained for the capacity of a surface obtained by Kelvin inversion of a prolate or an oblate spheroid. The surface thus obtained has the shape of either a blood cell or a peanut, both of which exhibit concavities. The capacity is found in terms of the solution of an interior problem for the spheroid through the Kelvin transformation with the centre of inversion at the midpoint of the interfocal line segment. The capacity is then used to describe the exact first two terms in a low-frequency expansion of the far field scattered by an acoustically-soft inverted spheroid when illuminated by a plane wave.