Dynamics Associated with the Normally Hyperbolic Invariant Manifold that Governs the Ionization of Hydrogen in a Circularly Polarized Electric Field

Abstract

The ionization of hydrogen in a circularly polarized electric field consists of the electron escaping over a rotating Stark saddle. The escape is mediated by the stable and unstable manifolds of a normally hyperbolic invariant manifold associated with the saddle. General principles guarantee the existence of this normally hyperbolic invariant manifold which is referred to as a transition state for energies close to the saddle. We use a numerical procedure to continue the transition state to high energies and study the dynamics restricted to the transition state. We find that for the strength of the electric field under consideration, the transition state persists to very high energies and the restricted dynamics remains amazingly regular. Our analysis moreover includes a study of homoclinic orbits connecting the transition state to itself.