Non-Hydrogenic Rydberg Atoms in Magnetic Fields

Abstract

The classical and quantal dynamics of non-hydrogenic Rydberg atoms in magnetic fields are investigated. Previous attempts to infer classical behaviour from quantum properties produced conflicting results: at low scaled energies (ε=−0.5) the nearest-neighbour statistics (NNS) were found to be at the chaotic (Wigner) limit while quantum phase-space distributions suggested a high degree of regularity. Here the classical limit is investigated directly by solving the equations of motion of the Diamagnetic Kepler problem (DKP) with an additional non-Coulombic model potential. It is found that typically trajectories are, over a long time-scale, ergodic. However over a shorter time-scale—in between collisions with the core—classical trajectories remain confined on the tori of the DKP. The origin of a well-known resonance in the NNS of hydrogen at ε= −0.316 is clarified by the comparison with the non-hydrogenic behaviour. However, the classical model only partially explains the quantum behaviour. The difficulties of quantizing such a system are discussed.