A diffusion model for classical chaotic compound scattering

Abstract

We consider the classical map proposed previously to be the exact classical analog of Rydberg molecules calculated with the approximations relevant to the multi-channel quantum defect theory. The resulting classical map is analyzed at energies above the threshold for the Rydberg electron. At energies very near to this threshold we find the possibility of bounded motion for positive energy due to conserved tori as well as the possibility of forming a compound system, i.e., a system where the particle is trapped for long times before emerging again to the continuum. The compound scattering displays unusual features for short-time behavior. A diffusion model explains these features.