Relation between singularity expansion method (SEM) and resonance scattering theory (RST)

In recent years there are two theories for the acoustic scattering:the Singularity Expansion Method (SEM), and the Resonance Scattering Theory (RST). In this paper, relation between these two theories was established. Taking examples of the acoustic scattering from the solid elastic cylinder and the sphere immersed in water, we prove that the RST can be directly derived from the SEM, so that these two theories are equivalent. Using the Mittag-Leffler theorem we expand the pure elastic scattering wave, extracted by isolating the rigid background from the total scattering wave, in an exact resonance expansion. We specially prove that the reradiation efficiency and the resonance width are nearly proportional to th imaginary part of the corresponding pole for most solid objects immersed in water. This shows that the resonance scattering behavious can be entirely determined by the complex frequency poles. For the cases of an aluminum cylinder and a tungsten carbide sphere immersed in water, we calculate the partial-wave form functions by using the new resonance formulae. The results agree with the exact calculation well.