Parabolic manifolds in the scattering map and direct quantum processes

Abstract

We analyse the quantum effects of parabolic manifolds in Jung's iterated scattering map. For this purpose we consider the classical map proposed previously to be the exact classical analogue of Rydberg molecules calculated with the approximations relevant to the multichannel quantum defect theory for energies above the ionization threshold. The part corresponding to positive electron energies can be viewed as a Jung scattering map without the trivial direct processes. This map contains a parabolic manifold of fixed points which gives rise to a regular series of quantum states which behave very much like eigenchannels that miss the target.