Radiative corrections to relativistic magnetic-dipole decays of hydrogenlike ions

Abstract

The radiative correction to the decay $2S_{\frac{1}{2}}\to 1S_{\frac{1}{2}}+1\mathrm{}\gamma$ in hydrogenlike atoms is calculated to relative order $\alpha$. All terms of order $\alpha \ln \alpha$ and $\alpha$ are found to cancel. The cancellation of the order-$\alpha$ terms does not occur in other relativistic $M1\mathrm{}$ transitions in hydrogenlike atoms.