SEMICLASSICAL ESTIMATION OF THE RADIATIVE MEAN LIFETIMES OF HYDROGENLIKE STATES

Based on the correspondence principle, a simple semiclassical derivation of a universal formula for the radiative mean lifetime tau(n,l) of hydrogenlike states is presented. (The possibilities of stimulated emission and collisional deexcitation are neglected.) Within the nonrelativistic dipole approximation the mean lifetime for an electron in a state characterized by quantum numbers n and l in the field of a nucleus of charge Z is given by tau(n,l) almost-equal-to tau-0n3l(l+1)/Z4, where tau-0 = 3h (2-alpha-5-mu-c2) almost-equal-to 93.42 X 10(-12) s and mu is the reduced mass. The formula is accurate to at least 6% for the lowest states and to a much higher degree of accuracy for highly excited states. The semiclassical result is expected to be valid to leading order in n and l. However, the very simple derivation yields results of an accuracy comparable to several approximate quantum-mechanical and semiclassical results that have been published. The approach is based primarily upon a treatment of the rate of loss of angular momentum, not of energy. A clear physical interpretation of some aspects of the radiative decay process, which is somewhat obscure in the quantum evaluation, emerges naturally from the angular momentum approach.