Relativistic Corrections to Radiative Transition Probabilities

The rate of spontaneous emission of radiation by a loosely bound composite system is calculated from quantum electrodynamics correct through terms of relative order ${\alpha }^2{Z}^2$. Recent criticisms by Feinberg and Sucher of the semiclassical method of deriving the higher-order radiation coupling terms are discussed. It is proved that the Breit interaction remains valid in the presence of radiation emission and that the semiclassical and quantum-electrodynamic methods of deriving the higher-order coupling terms always yield the same results to relative order ${\alpha }^2{Z}^2$. We discuss in particular relativistic corrections to allowed and spin-forbidden electric dipole transitions and the $1s2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1\mathrm{}{s}^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ magnetic dipole transition.