Classical calculation of radiative decay rates of hydrogenic Stark states

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 -Delta 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 Delta n. A simple approximate expression for the lifetime of m not equal 0 states emerges from the semi-classical analysis.

Automated summary

The Kepler-Coulomb problem is solved in parabolic coordinates, and the Larmor radiation problem is analyzed to complement a previous study in spherical polar coordinates. The study is extended to include a weak electric field, and a solution in terms of action-angle variables is provided. Comparison with quantum spontaneous decay rates shows that transitions to nearby principal quantum number states are accurately described by WKB quantized classic motions for m = 0 states, while reasonable results emerge for m > 0 for many values of Delta n. An approximate expression for the lifetime of m not equal 0 states is obtained from the semi-classical analysis.