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

In recent years there are two theories for the acoustic scattering,one isthe Singularity Expansion Method(SEM),the other is the Resonance Scat-tering Theory(RST).In this paper,relation between these two theories wasestablished.For the examples of the acoustic scattering from the solid elasticcylinder and sphere immersed in water,we prove that the RST can be directlyderived from the SEM,so that these two theories are equivalent.By use of theMittag-Leffler theorem we expand the pure elastic scattering wave,which isextracted by isolating the rigid background from the total scattering wave,in anexact resonance expansion.We specially prove that the reradiation efficiencyand the resonance width are nearly proportional to the imaginary part of thecorresponding pole for most solid objects immersed in water.This shows thatthe resonance scattering behavious can be entirely determined by the complexfrequency poles.For the cases of an aluminum cylinder and a tungsten carbidesphere immersed in water,we calculate the