Nuclear charge radius of $^{26m}$Al and its implication for V$_{ud}$ in the quark-mixing matrix

TL;DR

This study measured the nuclear charge radius of the isomer $^{26m}$Al using collinear laser spectroscopy, revealing a significant deviation from previous estimates, which impacts the precision of $V_{ud}$ in the CKM matrix.

Contribution

First experimental determination of the nuclear charge radius of $^{26m}$Al, providing crucial data for isospin-symmetry breaking corrections in superallowed beta decay.

Findings

Measured $^{26m}$Al charge radius: 3.130 ± 0.015 fm.

Discrepancy of 4.5 standard deviations from previous extrapolated value.

Shifted the corrected $ extit{Ft}$ value, affecting $V_{ud}$ estimation.

Abstract

Collinear laser spectroscopy was performed on the isomer of the aluminium isotope $^{26m}$Al. The measured isotope shift to $^{27}$Al in the $3s^{2}3p\;^{2}\!P^\circ_{3/2} \rightarrow 3s^{2}4s\;^{2}\!S_{1/2}$ atomic transition enabled the first experimental determination of the nuclear charge radius of $^{26m}$Al, resulting in $R_c$=\qty{3.130\pm.015}{\femto\meter}. This differs by 4.5 standard deviations from the extrapolated value used to calculate the isospin-symmetry breaking corrections in the superallowed $\beta$ decay of $^{26m}$Al. Its corrected $\mathcal{F}t$ value, important for the estimation of $V_{ud}$ in the CKM matrix, is thus shifted by one standard deviation to \qty{3071.4\pm1.0}{\second}.