Isospin corrections for superallowed Fermiβdecay in self-consistent relativistic random-phase approximation approaches

Abstract

Self-consistent random phase approximation (RPA) approaches in the relativistic framework are applied to calculate the isospin symmetry-breaking corrections ${\ensuremath{\delta}}_{c}$ for the ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ superallowed transitions. It is found that the corrections ${\ensuremath{\delta}}_{c}$ are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections ${\ensuremath{\delta}}_{c}$, the nucleus-independent $\mathcal{F}t$ values are obtained in combination with the experimental $\mathit{ft}$ values in the most recent survey and the improved radiative corrections. It is found that the constancy of the $\mathcal{F}t$ values is satisfied for all effective interactions employed. Furthermore, the element ${V}_{\mathit{ud}}$ and unitarity of the Cabibbo-Kobayashi-Maskawa matrix are discussed.