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Classical particle scattering for power-law two-body potentials

2016/01/01 by David Chiron, D Chiron, Chiron, D +3
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE) #High-Energy Particle Collisions Research #High-pressure geophysics and materials #Nuclear physics research studies #Statistical Mechanics (cond-mat.stat-mech) #astro-ph.HE #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.1601.00064

23 pages, 17 figures

arxiv created 2016/01/01 · openalex publication_date 2016/01/01 · arxiv updated 2016/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a rigorous study of the classical scattering for anytwo-body inter-particle potential of the form v(r)=g/rγ, withγ\textgreater0, for repulsive (g\textgreater0) and attractive (g\textless0)interactions. We give a derivation of the complete power series of thedeflection angle in terms of the impact factor for the weak scatteringregime (large impact factors) as well as the asymptotic expressionsfor the hard scattering regime (small impact factors). We see a verydifferent qualitative and quantitative behavior depending whether theinteraction is repulsive or attractive. In the latter case, thefamilies of trajectories depend also strongly on the value ofγ. We also study carefully the modifications of the resultswhen a regularization is introduced in the potential at small scales.We check and illustrate all the results with the exact integration ofthe equations of motion.

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