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. 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 −Δn 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 Δn. A simple approximate expression for the lifetime of m ≠ 0 states emerges from the semi-classical analysis.