We discuss the possibility of achieving abnormally low electromagnetic scattering cross sections at low frequencies by adjusting the optical properties of the scatterers (e.g., concentric spheres), generalizing the work in an earlier communication. The discussion is based upon an expansion valid for any spherical scatterer of finite size and is model independent. It is shown that if the electric and magnetic dipole scattering lengths are made to vanish, the low-frequency cross section is proportional to k8 for dielectric bodies, as has been observed experimentally in phase-separated glasses and in precipitated alloys. The angular distribution under these conditions is discussed, and is found normally to peak in the backward direction also in agreement with experiment.
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