Critical evaluation of reference charge radii and applications in mirror nuclei

TL;DR

This paper critically reviews and refines charge radii measurements of stable nuclei, establishes a proportional relation with isospin asymmetry for mirror nuclei, and predicts unknown mirror radii, aiding nuclear theory and fundamental tests.

Contribution

It provides a comprehensive, uncertainty-aware analysis of charge radii, confirms a linear relation with isospin asymmetry, and predicts radii for 73 unknown mirror nuclei, enhancing nuclear data accuracy.

Findings

Confirmed proportionality between mirror radii difference and isospin asymmetry.

Revised charge radii with overlooked uncertainties.

Predicted radii for 73 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 \textit{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 \emph{et al}~[PRL~130, 032501]. 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 testing of the unitarity of the CKM matrix.