The einstein a-coefficient of spontaneous emission: a relativistic calculation in the Heisenberg representation

Abstract

We present a simple approach to the relativistic calculation of the rates of spontaneous emission starting from the Heisenberg picture formula for the power radiated by a charged particle undergoing acceleration, and evaluate atomic decay rates using relativistic Dirac^Coulomb wavefunctions. The spin of the electron, embedded in its relativistic wavefunction, is shown to correctly provide the two polarization states of the emitted radiation. We discuss selection rules and calculate the Hydrogen 2P -t IS transition rate, among others, to be r = (6.2650 ±0.0007) x 10 V in good agreement with the full field theory calculation as well as with experiment.