A New Approximate Formula for Scattering of Plane Acoustic Waves by a Spherical Obstacle

A new approximate formula for scattering amplitude of a plane acoustic wave by a sphere is presented. It is based on a similar formula introduced long ago by Hart and Montroll in the context of scattering of light by a sphere. The scattering amplitude is shown to consist of two terms. The first term is related to the scattering amplitude in the modified Born approximation, a variant of the well known Born approximation. The second term constitutes a correction which is of the order of impedance mismatch between the scatterer and the surrounding medium. Numerical comparisons of this formula with exact results have been performed. It is shown that the new approximation betters the modified Born approximation and other variants of the Born approximation as the weak scatterer condition for the validity of Born type approximations is relaxed.