Accurate Charge Radius Measurement of C Confronts \textit{Ab Initio} Theory
Kristian König🇩🇪 · Patrick Müller🇩🇪 · Tobias Gesser · Emily Burbach🇩🇪 · Stefano Gandolfi🇺🇸 · Matthias Heinz🇺🇸 · Phillip Imgram🇩🇪 · Alessandro Lovato🇺🇸 · Pieter Maris🇺🇸 · Takayuki Miyagi🇩🇪 · Wilfried Nörtershäuser🇩🇪 · Robert Roth🇩🇪 · Julien Spahn🇩🇪 · Achim Schwenk🇩🇪
Located at the neutron shell closure , the long-lived radioactive isotope \(^{14}\mathrm{C} \) plays a critical role in geochronology and nuclear structure studies. Despite its widespread use, the nuclear charge radius of C has remained less precisely known compared to its stable counterpart C. Here, we report a high-precision determination of the C charge radius using collinear laser spectroscopy at the COALA setup at TU Darmstadt, improving upon the precision of previous muonic measurements by a factor and revealing a discrepancy of combined uncertainty, indicating a likely underestimated uncertainty in the muonic determination. This measurement challenges state-of-the-art \textit{ab initio} nuclear theory calculations, including auxiliary field diffusion Monte Carlo, the valence-space in-medium similarity renormalization group, and the no-core shell model, augmented by neural-network techniques. With C and C now forming one of the most precisely characterized even-even isotope pairs, these results also enable improved QED tests.