Series expansions of the deflection angle in the scattering problem for power-law potentials

Description

We present a rigorous study of the classical scattering for any two-body inter-particle potential of the form v(r) = g/r^γ , with γ > 0, for repulsive (g > 0) and attractive (g < 0) interactions. We first derive an explicit series expansion of the deflection angle in the impact factor b. Then, we study carefully the modifications of the results when a regularization (softening) is introduced in the potential at small scales. We check and illustrate all the results with the exact integration of the equations of motion.

Abstract

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