Elastic Scattering of Point Particles With Nearly Equal Masses

TL;DR

This paper investigates the collision behavior of n billiard particles with nearly equal masses, demonstrating the existence of specific open sets in phase and mass space where particular collision counts occur, even near equal mass configurations.

Contribution

It establishes the existence of open sets in phase and mass space where particles exhibit prescribed collision counts, extending understanding of collision dynamics for nearly equal masses.

Findings

Existence of open sets with specific collision counts

Open sets intersect neighborhoods of equal mass configurations

Results apply to n particles on a line

Abstract

We show that for n billiard particles on the line there exist three open sets in the product of phase space and the space of their masses, such that these particles exhibit exactly n-1, n over 2 respectively n+1 over 3 collisions. These open sets intersect any neighborhood of the diagonal in mass space.