QED calculations of the nuclear recoil effect in muonic atoms

TL;DR

This paper presents precise QED calculations of the nuclear recoil effect in muonic atoms, crucial for accurate nuclear charge radius extraction from spectral data, highlighting differences from previous approximations especially for low-lying states.

Contribution

The authors perform all-order QED calculations of the nuclear recoil effect in muonic atoms, improving accuracy over previous approximate methods.

Findings

Recoil correction differs significantly from earlier approximations for low-lying states.

Calculated recoil correction is sensitive to nuclear charge radius.

Results improve the theoretical foundation for extracting nuclear parameters.

Abstract

The nuclear recoil effect, known also as the mass shift, is one of theoretical contributions to the energy levels in muonic atoms. Accurate theoretical predictions are therefore 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 $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ 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 the measured spectra.