PARABOLIC MANIFOLDS IN THE SCATTERING MAP AND DIRECT QUANTUM PROCESSES

We analyse the quantum effects of parabolic manifolds in Jung's iterat ed scattering map. For this purpose we consider the classical map prop osed previously to be the exact classical analogue of Rydberg molecule s calculated with the approximations relevant to the multichannel quan tum defect theory for energies above the ionization threshold. The par t 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 Axed points which gives rise to a regular ser ies of quantum states which behave very much like eigenchannels that m iss the target.