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In this paper, the translational addition theorem for spherical functions isemployed to exactly calculate the acoustic radiation force produced by anarbitrary shaped beam on a sphere suspended in an inviscid fluid. The radiationforce is given in terms of the beam-shape and the scattering coefficients. Eachbeam-shape coefficient (BSC) is the complex weight of a multipole mode inpartial-wave expansion of the incident beam. Moreover, they depend on thechoice of the reference frame which is defined by the sphere's center. On theother hand, the scattering coefficients are obtained from the acoustic boundaryconditions across the sphere's surface. Given a set of known BSCs, thetranslational addition theorem can be used to obtain the new coefficientsrelative to the sphere's position. Such approach is particularly useful when noclosed-form expression of the incident pressure is known, but its BSCs areavailable. This is the case of a spherically focused ultrasound beam, for whichwe compute the radiation force on an absorbing compressible sphere arbitrarlyplaced in the fluid. The analysis is carried out in the Rayleigh and theresonant scattering regimes. It is shown that the focused beam may trap aspherical particle in the Rayleigh scattering regime.

Exact computations of the acoustic radiation force on a sphere using the translational addition theorem