Nonhydrogenic Rydberg atoms in a magnetic field: A rigorous semiclassical approach.

Multielectron atoms in external fields are essentially more complicated than hydrogen with regard to theoretical treatments. Experimental spectra of helium as well as R-matrix quantum-defect calculations revealed discrepancies between the diamagnetic hydrogen atom and general Rydberg atoms. They appeared most transparent as novel resonance structures in constant scaled-energy recurrence spectra of nonhydrogenic atoms at positions where no hydrogenic resonances exist. To reveal the physical origin of these resonances we performed a rigorous semiclassical investigation of nonhydrogenic atoms in magnetic fields. The ionic core is introduced into the Hamiltonian via a short-ranged core potential. For this Hamiltonian we analyze in detail the classical dynamics of closed orbits. Classical core-scattering results in the creation of a huge number of new closed orbits. They appear to be composed of a sequence of slightly different hydrogenic orbits, interconnected by the core-scattering, and can be grouped into families accordingly. With a semiclassical closed-orbit theory generalized to arbitrary quantum defects of the ionic core and with the closed orbits at hand we are able to calculate photoabsorption spectra of nonhydrogenic atoms. Although each of the new orbits has a low amplitude, the interference of all members of a family results in clearly visible resonances in the Fourier transform recurrence spectra, in good agreement with experiment and quantum calculations. The novel structures in nonhydrogenic spectra are now identified and semiclassically interpreted in terms of families of core-scattered classical orbits.