Classical calculation of radiative decay rates of hydrogenic Stark states

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. A comparison with quantum spontaneous decay rates shows that for azimuthal quantum number $m=0$ states only transitions to nearby $n-\Delta n$ principal quantum number states are described properly by the Wentzel-Kramers-Brillouin quantized classical motions, but that for $m>0$ reasonable results emerge for many values of $\Delta n$. A simple approximate expression for the lifetime of $m\ne 0$ states emerges from the semi-classical analysis.

37 pages, 8 figures, 44 references; revised after referee reports from J Phys B

References in corpus (2)

• Visualization and interpretation of Rydberg states
• The trouble with orbits: the Stark effect in the old and the new quantum theory

Cited by in corpus (1)

• Classical versus quantum calculation of radiative electric quadrupole transition rates for hydrogenic states