Contrast factor for standing-wave radiation forces on spheres: Series expansion in powers of sphere radius

Recently researchers often normalize the radiation force on spheres in standing waves in inviscid fluids using an acoustic contrast factor (typically denoted by Φ) that is independent of kR where k is the wave number and R is the sphere radius. An alternative normalization uses a function Ys that depends on kR. Here, standard results for Φ are extended as a power series in kR using prior Ys results. Also, new terms are found for fluid spheres and applied to the kR dependence of Φ for strongly responsive and weakly responsive examples. Partial-wave phase shifts are used in the derivation.