Relativistic recoil as a key to the fine-structure puzzle in muonic 90Zr

Abstract Muonic atoms provide one of the most sensitive probes of nuclear charge distributions and stringent tests of bound-state quantum electrodynamics (QED). Their full potential has been compromised by a long-standing fine-structure anomaly in heavy muonic atoms, hindering the reliable interpretation of precision spectroscopic data. Here we show that the manifestation of this anomaly in 90 Zr is resolved by a complete treatment of the relativistic-recoil effect. Fitting ab initio QED calculations to precision measurements of the muonic 90 Zr spectrum performed four decades ago yields a root-mean-square charge radius of r rms [ 90 Zr] = 4.2732(7) fm, improves the quality of the fit by a factor of four, and reduces the uncertainty of the extracted radius by a factor of six. The resulting charge radius is consistent with the previous value from muonic spectroscopy but more than 3 σ larger than the accepted literature value. Applying the same analysis to 120 Sn yields r rms [ 120 Sn] = 4.6518(34) fm, in agreement with the accepted value. These results show that the long-standing fine-structure anomaly originated from an incomplete treatment of QED effects, restoring the predictive power of muonic-atom spectroscopy.