  The near-field acoustic scattering from a sphere centered on the axis of a
finite Bessel acoustic beam is derived stemming from the Rayleigh-Sommerfeld
diffraction surface integral and the addition theorems for the spherical wave
and Legendre functions. The beam emerges from a finite circular disk vibrating
according to one of its radial modes corresponding to the fundamental solution
of a Bessel beam J0. The incident pressure field's expression is derived
analytically as a partial-wave series expansion taking into account the finite
size and the distance from the center of the disk transducer. Initially, the
scattered pressure by a rigid sphere is evaluated, and backscattering pressure
moduli plots as well as 3-D directivity patterns for an elastic PMMA sphere
centered on a finite Bessel beam with appropriate tuning of its half-cone
angle, reveal possible resonance suppression of the sphere only in the zone
near the Bessel transducer. Moreover, the analysis is extended to derive the
mean spatial incident and scattered pressures at the surface of a rigid
circular receiver of infinitesimal thickness. The transducer, sphere and
receiver are assumed to be coaxial. Some applications can result from the
present analysis since all physically realizable Bessel beam sources radiate
finite sound beams as opposed to waves of infinite extent.
