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

摘要

We present a rigorous study of the classical scattering for any two-body interparticle potential of the form v(r) = g/r(gamma) with gamma > 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. Published under license by AIP Publishing.