Classical calculation of radiative decay rates of hydrogenic Stark states

TL;DR

This paper provides a classical calculation of radiative decay rates for hydrogenic Stark states, comparing semi-classical results with quantum decay rates, and deriving approximate lifetimes for certain states.

Contribution

It extends classical methods to compute decay rates of Stark states and offers an approximate lifetime formula for states with non-zero azimuthal quantum number.

Findings

Classical calculations align with quantum results for specific states.

Transitions to nearby principal quantum numbers are well-described for m=0.

Approximate lifetimes for m≠0 states are derived from semi-classical analysis.

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.