Collinear electron-helium-ion collisions: Chaotic scattering dominated by triple-collision orbits.

Abstract

We study the fractal scattering patterns of collinear collisions between an electron and a helium ion or a hydrogen atom. We have found that the collisional time plotted against initial energy or initial phase consists of a bi-infinite sequence of cusp-shaped regular intervals interlaced by chaotic bands and repeated enlargements of the chaotic bands show similar patterns. These patterns resemble the previous ones obtained in the retrograde region of the coplanar scattering system, however, the dynamical origin of the self-similar patterns is different and can be understood in terms of various combinations of motions perpendicular and parallel to the Wannier ridge and binary collisions. In particular, we have found that the trajectories near the cusp tips of regular intervals are strongly influenced by a set of triple-collision orbits, trajectories originate and end at the triple-collision point. Using the code and winding number for these orbits, we can organize the fractal scattering patterns into a tree structure. Furthermore, using an ensemble of trajectories with uniformly selected initial phases, we calculate the transition probabilities of excited electronic states from a certain initial state of the hydrogenlike ion or atom using the quasiclassical trajectory method. These transition probabilities illustrate that chaotic regions on the average correspond to higher electronic excitation than that corresponding to the regular regions. \textcopyright{} 1996 The American Physical Society.