Classical Mechanics of Collinear Positron-Hydrogen Scattering

TL;DR

This paper analyzes the classical chaotic dynamics of collinear positron-hydrogen scattering below the three-body breakup threshold, revealing phase space invariances, stable orbits, and potential quantum implications.

Contribution

It introduces a new code system and surface of section for phase space analysis, uncovering invariance under variable exchange and identifying stable periodic orbits.

Findings

Chaotic scattering time signals observed

Phase space structure invariant under variable exchange

Stable shortest periodic orbit identified

Abstract

We study the classical dynamics of the collinear positron-hydrogen scattering system below the three-body breakup threshold. Observing the chaotic behavior of scattering time signals, we in- troduce a code system appropriate to a coarse grained description of the dynamics. And, for the purpose of systematic analysis of the phase space structure, a surface of section is introduced being chosen to match the code system. Partition of the surface of section leads us to a surprising conjec- ture that the topological structure of the phase space of the system is invariant under exchange of the dynamical variables of proton with those of positron. It is also found that there is a finite set of forbidden patterns of symbol sequences. And the shortest periodic orbit is found to be stable, around which invariant tori form an island of stability in the chaotic sea. Finally we discuss a possible quantum manifestation of the classical phase space structure relevant to resonances in scattering cross sections.