Scattering and radiation force dependence on properties of empty elastic spherical shells: Low-frequency phase-shift derivation

It is helpful to evaluate scattering and acoustic radiation forces on spheres for idealized cases in which the effects of energy dissipation are ignorable. Let x denote the product of the acoustic wave number and the sphere's radius. Previously expansions were obtained for fluid and solid spheres involving powers of x and algebraic expressions containing material properties. The present analysis concerns the case of empty elastic shells and reveals how expansion coefficients also depend on shell thickness. Incident waves considered are plane traveling and standing waves, though relevance to Bessel wave-fields is also noted. The expansions give leading-order corrections to the usual Rayleigh scattering approximation.