COLLINEAR ELECTRON-HELIUM-ION COLLISIONS - CHAOTIC SCATTERING DOMINATED BY TRIPLE-COLLISION ORBITS

We study the fractal scattering patterns of collinear collisions betwe en 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 in terlaced by chaotic bands and repeated enlargements of the chaotic ban ds show similar patterns. These patterns resemble the previous ones ob tained in the retrograde region of the coplanar scattering system, how ever, the dynamical origin of the self-similar patterns is different a nd can be understood in terms of various combinations of motions perpe ndicular and parallel to the Wannier ridge and binary collisions. In p articular, we have found that the trajectories near the cusp tips of r egular 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 th e fractal scattering patterns into a tree structure. Furthermore, usin g 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 th e quasiclassical trajectory method. These transition probabilities ill ustrate that chaotic regions on the average correspond to higher elect ronic excitation than that corresponding to the regular regions.