AN ANALYTIC SOLUTION FOR LOW-FREQUENCY SCATTERING BY 2 SOFT SPHERES

A plane wave is scattered by two small spheres of not necessarily equa l radii. Low-frequency theory reduces this scattering problem to a seq uence of potential problems which can be solved iteratively. It is sho wn that there exists exactly one bispherical coordinate system that fi ts the given geometry. Then R-separation is utilized to solve analytic ally the potential problems governing the leading two low-frequency ap proximations. It is shown that the Rayleigh approximation is azimuthal independent, while the first-order approximation involves the azimuth al angle explicitly. The leading two nonvanishing approximations of th e normalized scattering amplitude as well as the scattering cross-sect ion are also provided. The Rayleigh approximations for the amplitude a nd for the cross-section involve only a monopole term, while their nex t order approximations are expressed in terms of a monopole as well as a dipole term. The dipole term disappears whenever the two spheres be come equal, and this observation provides a way to determine whether t he two spheres are equal or not, from far-field measurements. Finally, it is shown that for all practical purposes, first-order multiple sca ttering yields an excellent approximation of this scattering process.