  Based on the partial-wave series expansion (PWSE) method in spherical
coordinates, a formal analytical solution for the acoustic scattering of a
zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate)
spheroid is provided. The unknown scattering coefficients of the spheroid are
determined by solving a system of linear equations derived for the Neumann
boundary condition. Numerical results for the modulus of the backscattered
pressure (\theta = \pi) in the near-field and the backscattering form function
in the far-field for both prolate and oblate spheroids are presented and
discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the
major axis over the minor axis of the spheroid), the half-cone angle of the
Bessel beam \beta, and the dimensionless frequency. The plots display periodic
oscillations (versus the dimensionless frequency) due to the interference of
specularly reflected waves in the backscattering direction with circumferential
Franz' waves circumnavigating the surface of the spheroid in the surrounding
fluid. Moreover, the 3D directivity patterns illustrate the near and far-field
axisymmetric scattering. Investigations in underwater acoustics, particle
levitation, scattering, and the detection of submerged elongated objects and
other related applications utilizing Bessel waves would benefit from the
results of the present study.
