$^{208}$Pb nuclear charge radius revisited: closing the fine-structure-anomaly gap

Abstract

A comprehensive reevaluation of the root-mean-square nuclear charge radius is presented for the doubly magic $^{208}$Pb extracted from muonic spectroscopy measurements. By integrating rigorous theoretical quantum electrodynamics calculations, state-of-the-art numerical methods, and a systematic reanalysis of the uncertainties, we reduced the long-standing muonic fine-structure anomaly and improved the goodness of fit by a factor of twenty. The resulting value of 5.5062(5)~fm for a Fermi distribution is fairly consistent with the previously reported muonic spectroscopy value, and three standard deviations larger than the commonly used compilation data, which indicates that the current value and its uncertainty could be significantly underestimated. Attributing the remaining discrepancy to theory errors which can not be rigorously calculated we suggest the rms charge radius with reduced model dependence to be 5.5062(17) fm. This work sets an improved benchmark for charge radius extraction in heavy nuclei and paves a path for systematic reevaluations across the nuclear chart.