Classical calculation of radiative decay rates of hydrogenic Stark states. (23rd April 2021)

• Record Type: Journal Article
• Authors: Horbatsch, Michael; Horbatsch, Marko
• Is Part Of: Journal of physics. Volume 54:Number 6(2021)
• Publication Date: 2021-04-23
• Subjects: quantum–classical correspondence -- radiative decays -- semi-classical quantization -- Rydberg–Stark states; Atoms -- Periodicals; Molecules -- Periodicals; Optics -- Periodicals; Nuclear physics -- Periodicals; 539.6
• DOI: 10.1088/1361-6455/abe0a5
• Languages: English
• ISSNs: 0953-4075

Abstract

Abstract: The Kepler–Coulomb problem is solved in parabolic coordinates and the Larmor radiation problem is analyzed to complement a previous study performed for the usual representation in spherical polar coordinates. The problem is then extended to include a weak electric field and a solution in terms of action-angle variables is provided. A comparison with quantum spontaneous decay rates shows that for azimuthal quantum number m = 0 states only transitions to nearby n −Δ n principal quantum number states are described properly by the Wentzel–Kramers–Brillouin (WKB) quantized classical motions, but that for m > 0 reasonable results emerge for many values of Δ n . A simple approximate expression for the lifetime of m ≠ 0 states emerges from the semi-classical analysis.