Beyond Periodic Orbits: An Example in Nonhydrogenic Atoms

Abstract

The spectrum of hydrogen in a magnetic field is a paradigm of quantum chaos and may be analyzed accurately by periodic-orbit-type theories. In nonhydrogenic atoms, the core induces pure quantum effects, especially additional spectral modulations, which cannot be analyzed reliably in terms of classical orbits and their stability parameters. Provided core-scattered waves are included consistently, core-scattered modulations as well as corrected amplitudes for primitive orbits are in excellent agreement with quantum results. We consider whether these systems correspond to quantum chaos.

Rydberg Molecules in External Fields: A Semiclassical Analysis

“…For µ Σ = µ Π = 0.5 [ Fig. 2(b)], elastic core scattering between ǫ N =0 orbits produces the additional peaks; these combination orbits were seen in non-hydrogenic atomic spectra [5]. (c) shows µ Σ = 0.5, µ Π = −0.5, in which case Eqs.…”

“…Originally devised for hydrogen, COT was later extended to singly excited non-hydrogenic ('Rydberg') atoms [4,5], accounting for the presence of the ionic core. It was found [5] that the core-scattering produces additional 'combination' orbits. Non-hydrogenic energy-level spectra, even in weak fields where the classical dynamics for hydrogen is near-integrable, were found to be significantly more complex, showing short-range level repulsion and a proliferation of spectral modulations, a behavior termed 'core-induced chaos'.…”

“…However, analysis of the photoabsorption spectra from a low-lying initial state, require Closed-orbit theory (COT) [4], a semiclassical description of a density of states weighted by a dipole matrix element. Originally devised for hydrogen, COT was later extended to singly excited non-hydrogenic ('Rydberg') atoms [4,5], accounting for the presence of the ionic core. It was found [5] that the core-scattering produces additional 'combination' orbits.…”

“…These arise from inelastic scattering between the core and the outer electron and appear at a scaled action corresponding to the sum of an ǫ N =2 orbit (or its repetitions) and an ǫ N =0 orbit. The shortest of these combination orbits occurs at S = 1.71 and combines the V 1 1 'balloon orbit' [5] at ǫ = −0.3 [peak '1' in Fig. 2(a)] with the primitive orbit 'i' at ǫ = −2.45 [the first peak in Fig.…”

Scaled-Energy Spectroscopy of Helium and Barium Rydberg Atoms in External Fields

“…For highly-excited states this involves the diagonalization of huge energy matrices, for which special numerical techniques have been developed [8,9]. Such calculations are also possible under conditions of constant-scaled energy, so that a direct comparison with experimental data and Fourier transforms can be made.…”