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

In this paper, the translational addition theorem for spherical functions is employed to exactly calculate the acoustic radiation force produced by an arbitrary shaped beam on a sphere suspended in an inviscid fluid. The radiation force is given in terms of the beam-shape and the scattering coefficients. Each beam-shape coefficient (BSC) is the complex weight of a multipole mode in partial-wave expansion of the incident beam. Moreover, they depend on the choice of the reference frame which is defined by the sphere's center. On the other hand, the scattering coefficients are obtained from the acoustic boundary conditions across the sphere's surface. Given a set of known BSCs, the translational addition theorem can be used to obtain the new coefficients relative to the sphere's position. Such approach is particularly useful when no closed-form expression of the incident pressure is known, but its BSCs are available. This is the case of a spherically focused ultrasound beam, for which we compute the radiation force on an absorbing compressible sphere arbitrarly placed in the fluid. The analysis is carried out in the Rayleigh and the resonant scattering regimes. It is shown that the focused beam may trap a spherical particle in the Rayleigh scattering regime.