Classical mechanics of collinear positron-hydrogen scattering

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