Relativistic theory of spontaneous emission

We derive a formula for the relativistic decay rates in atoms in a formulation of quantum electrodynamics based upon the electron’s self-energy. Relativistic Coulomb wave functions are used, the full spin calculation is carried out, and the dipole approximation is not employed. The formula has the correct nonrelativistic limit and is used for calculating the decay rates in hydrogen and muonium for the transitions 2P→1$S_{1/2}$ and 2$S_{1/2}$→1$S_{1/2}$. The results for hydrogen are Γ(2P→${1S}_{1/2}$)=6.2649×${10}^8$ ${\mathrm{s}}^{\mathrm{-}1}$ and Γ(${2S}_{1/2}$→${1S}_{1/2}$)=2.4946×${10}^{-6}$. Our result for the 2P→1S transition rate is in perfect agreement with the best nonrelativistic calculations as well as with the results obtained from the best known radiative decay lifetime measurements. As for the hydrogen 2$S_{1/2}$→1$S_{1/2}$ decay rate, the result obtained here is also in good agreement with the best known magnetic dipole calculations. For muonium we get Γ(2P→${1S}_{1/2}$)=6.2382×${10}^8$ ${\mathrm{s}}^{\mathrm{-}1}$ and Γ(${2S}_{1/2}$→${1S}_{1/2}$)=2.3997×${10}^{-6}$ ${\mathrm{s}}^{\mathrm{-}1}$.