Classical Scattering and Block Regularization for the Homogeneous Central Field Problem

Abstract

The present paper offers an alternative point of view of block regularization for the motion of a particle in a central potential field of the form −x −α, where x is the distance between the particle and the source and α some positive real number. Working in the physical space, we consider the scattering angle determined by the path of the particle as a function of angular momentum. We prove that a particle flow is passing over the collision singularity preserving differentiability with respect to initial data if and only if α = 2(1−1/n), n positive integer, n ≥ 2. This result coincides with the outcome of block regularization applied by McGehee to the same dynamical problem. We discuss that this identity was to expect since both methods target the same physical constraint over the flow.