Self-consistent random phase approximation (RPA) approaches in the relativistic framework are applied to calculate the isospin symmetry-breaking corrections ${\delta }_c$ for the $0^{+}\to 0^{+}$ superallowed transitions. It is found that the corrections ${\delta }_c$ are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections ${\delta }_c$, 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.

• Received 23 April 2009

DOI:https://doi.org/10.1103/PhysRevC.79.064316