Isospin corrections for superallowed Fermi beta decay 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 ${\delta }_c$ 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 $ft$ 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 $V_{ud}$ and unitarity of the Cabibbo-Kobayashi-Maskawa matrix are discussed.

7 pages, 2 figures, 4 tables

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