Rydberg States

We have considered a simple model for a high molecular Rydberg state in two different energy regimes. High Rydberg states above n=100, where the electron is slower than even the rotations of most molecules and Rydberg states in the intermediate energy regime 10<n<30, where the electron is faster than the rotations but still slower than the vibrations. The major difference between the two energy regimes is in the nature of the coupling to the molecular degrees of freedom and in the implications of the presence of external fields. The Hamiltonian we used is that of a diatomic-like ionic core about which the electron revolves. The primary coupling is due to the anisotropic part of the potential which can and does induce energy and angular momentum exchanges between the orbital motion of the electron and the rotational-vibrational motion of the ionic core. We used classical trajectories in action-angle variables to validate the proposed interpretations and to probe the nature of the possible intramolecular decay channels. The classical picture provides a realistic approximation to the quantum evolution of the system at the very high end of the energy spectrum, i.e. for high Rydberg states. When resonances are important, i.e. for Rydberg states in the intermediate energy regime, a semiclassical approach was taken.

Based on the results obtained from the classical trajectory simulations, we derive an iterated map which mimics the dynamics. The map provides a very efficient way to numerically simulate the motion, but its main advantage is in that it can delineate the various coupling parameters that govern the dynamics. The full map was further reduced to a Fokker-Planck equation by invoking a random-phase approximation. Based on the Fokker-Planck description, analytical expressions for the nonradiative lifetime of the Rydberg state at both energy regimes were obtained.