Critical evaluation of reference charge radii and applications in mirror nuclei

Abstract

I present a critical review of absolute root-mean-square charge radii of stable nuclei from $Z=3$ to $Z=32$, which includes a previously overlooked uncertainty in the combined analysis of muonic x-ray and electron scattering experiments. From these reference radii and isotope shift measurements, I obtain those of 12 mirror pairs with a traceable and realistic uncertainty budget. The difference in radii between mirror nuclei is found to be proportional to the isospin asymmetry, confirming recent calculations by Novario et al. (2023). Assuming that this linear relation holds across the nuclear chart, the fitted proportionality constant, combined with the revised known radii, predicts the radii of 73 previously unknown mirror partners. These are useful e.g., for benchmarking atomic and nuclear theory, calibrating entire chains, and as an input to nuclear beta-decay calculations. The radii of $(T=1,T_z=0)$ nuclei are interpolated assuming negligible isospin symmetry breaking. This completes a model-independent, high-precision extraction of the charge and weak radii of all nuclei involved in the test of the unitarity of the CKM matrix.