Inelastic inverse chaotic scattering problem

Abstract

We consider the inverse scattering problem for a chaotic system as the task to reconstruct information about the chaotic invariant set from the knowledge of scattering data. In this Letter we show how a recent method developed for periodically driven systems can be modified to work for inelastic scattering of the type which occurs in vibrational excitation of molecules during collisions. The additional idea is to measure the total time and final momentum of the trajectories. In a corresponding two-dimensional plot, the occurring values fall naturally into disjoint groups easily related to the hierarchical levels of the scattering functions. We pay special attention to the effect of anharmonicity of the internal degree of freedom on the procedure of reconstruction.