Equivalence of expressions for the acoustic scattering of a progressive high-order bessel beam by an elastic sphere

The exact analytical solution for the acoustic scattering of a high-order (commonly known as generalized) Bessel beam (HOBB) by an elastic sphere immersed in an ideal fluid and centered along the beam axis is revisited. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis, the order, and the half-conical angle of the wave number components of the generalized Bessel beam. Using an appropriate grouping of terms, the expressions for the incident and scattered pressures, as well as the scattering (complex) form function provided in a recent work are transformed into expressions involving the partial wave series starting from the order m of the generalized Bessel beam. In this new formulation, the scattering coefficients for a HOBB are found to equal those obtained from the study of sound scattering of plane progressive waves by an elastic sphere. This suggests that the (complex) form function presented here may be used to advantage toward studying the acoustic scattering of a HOBB by spherical shells, coated spheres, and coated spherical shells using their corresponding scattering partial wave coefficients available in standard and recent literature texts.