  This work focuses on the interaction of an acoustical quasi-Gaussian beam
centered on a rigid immovable sphere, during which at least three physical
phenomena arise, namely, the (axial) acoustic scattering, the instantaneous
force, and the time-average radiation force which are investigated here. The
quasi-Gaussian beam is an exact solution of the source free Helmholtz wave
equation and is characterized by an arbitrary waist w0 and a diffraction
convergence length known as the Rayleigh range z_R. Specialized formulations
for the scattering and the instantaneous force function as well as the
(time-averaged) radiation force function are provided. Numerical computations
illustrate the variations of the backscattering form-function, the
instantaneous force function and the (time-averaged) radiation force function
versus the dimensionless frequency ka (where k is the wave number and a is the
radius of the sphere), and the results show significant differences from the
plane wave limit when the dimensionless beam waist parameter kw0 < 25. The
radiation force function may be used to calibrate high-frequency transducers
operating with this type of beam. Furthermore, the theoretical analysis can be
readily extended to the case of other types of spheres (i.e. elastic,
viscoelastic, shells, coated spheres and shells) providing that their
appropriate scattering coefficients are used.
