General theory of radiative corrections to atomic decay rates

A general expression is derived for the radiative corrections to the one-photon decay rates of hydrogen-like ions. Our approach is based on the evaluation of the imaginary part of the fourth-order Lamb shift for excited states. We thereby avoid the ambiguities connected with electron wave function renormalization. The result may be cast in a form which is manifestly gauge invariant. As an application, we show that the formulas used by Lin and Feinberg in their study of relativistic M1 transitions, obtained by heuristic arguments, are derivable from first principles.