General Rydberg Atoms in Crossed Electric and Magnetic Fields: Calculation of Semiclassical Recurrence Spectra with Special Emphasis on Core Effects

Abstract

The photoabsorption spectra of highly excited Rydberg atoms in external fields are known to be related to closed classical orbits of the excited electron. For atoms in a pure magnetic field, scaled recurrence spectra have successfully been calculated from classical orbits using the semiclassical closed-orbit theory. Rydberg atoms in crossed fields are more complicated as regards their theoretical and numerical treatment, as the Hamiltonian is nonseparable in three degrees of freedom, in contrast to only two nonseparable degrees of freedom in a pure magnetic field. In this paper, we present an extension of the closed-orbit theory to three degrees of freedom, taking into account arbitrary quantum defects. Motivated by nonhydrogenic resonances discovered in experimental scaled recurrence spectra of rubidium atoms, we investigate the influence of the ionic core on the three-dimensional closed orbits, using a simple model potential. We find that the introduction of a core potential results in an extreme increase of the number of closed orbits as compared to hydrogen. The novel orbits appear to be composed of hydrogenic orbits and are created through scattering by the core potential. Investigating the classical deflection function of the model potential, general properties of the new orbits can be explained. With the closed-orbit theory extended to three nonseparable degrees of freedom, we are able to calculate scaled recurrence spectra for Rydberg atoms in crossed fields with arbitrary quantum defects. Our results are in good agreement with the experimental spectra. In particular, the nonhydrogenic resonances can be explained in terms of the new orbits created by classical core scattering.