Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields

Abstract

The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n-manifold. By means of a detailed semiclassical analysis of the quantum spectrum, we demonstrate that it is the abundance of bifurcations of closed orbits that precludes the resolution of finer details. They necessitate the inclusion of uniform semiclassical approximations into the quantization process. Uniform approximations for the generic types of closed-orbit bifurcation are derived, and a general method for including them in a high-resolution semiclassical quantization is devised.

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Cited by in corpus (9)

• Exceptional Points in Atomic Spectra
• Exceptional points in the spectra of atoms in external fields
• Scaling laws for the photo-ionisation cross section of two-electron atoms
• Closed orbits and their bifurcations in the crossed-fields hydrogen atom
• Photodetachment of H${}^{-}$ by a Short Laser Pulse in Crossed Static Electric and Magnetic Fields
• Evidence of triple collision dynamics in partial photo-ionisation cross sections of helium
• Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits
• Fictitious time wave packet dynamics: II. Hydrogen atom in external fields
• Uniform semiclassical approximations on a topologically non-trivial configuration space: The hydrogen atom in an electric field