QED calculations of the nuclear recoil effect in muonic atoms

The nuclear recoil effect, known also as the mass shift, is one of the theoretical contributions to the energy levels in muonic atoms. Accurate theoretical predictions are needed for extracting, e.g., the nuclear charge radii from experimental spectra. We report rigorous QED calculations of the nuclear recoil correction in muonic atoms, carried out to all orders in the nuclear binding strength parameter $Z\ensuremath{\alpha}$ (where $Z$ is the nuclear charge number and $\ensuremath{\alpha}$ is the fine-structure constant). The calculations show differences with the previous approximate treatment of this effect, most pronounced for the lowest-lying bound states. The calculated recoil correction was found to be sensitive to the nuclear charge radius, which needs to be accounted for when extracting nuclear parameters from measured spectra.