We revisit the extraction of the $|V_{ ud}|$ CKM matrix element from the superallowed transition decay rate of $^{ 26m}$Al$\rightarrow$$^{ 26}$Mg, focusing on finite nuclear size effects. The decay rate dependence on the $^{ 26m}$Al charge radius is found to be four times higher than previously believed, necessitating precise determination. However, for a short-lived isotope of an odd $Z$ element such as $^{ 26m}$Al, radius extraction relies on challenging many-body atomic calculations. We performed the needed calculations, finding an excellent agreement with previous ones, which used a different methodology. This sets a new standard for the reliability of isotope shift factor calculations in many-electron systems. The $\mathcal{ F}t$ value obtained from our analysis is lower by $2.2\,\sigma$ than the corresponding value in the previous critical survey, resulting in an increase in $|V_{ ud}|^2$ by $0.9\,\sigma$. Adopting $|V_{ ud}|$ from this decay alone reduces the CKM unitarity deficit by one standard deviation, irrespective of the choice of $|V_{ us}|$.
Categories: nucl-th hep-ph nucl-ex physics.atom-ph physics.comp-ph