Test of the Standard Electroweak Model in superallowed 0$^{+ }\to $ 0$^{+}$ nuclear $\beta $ decays

Precise measurements of superallowed $\beta $ decays provide demanding test of the fundamental symmetries of the electroweak interaction. Collectively, the corrected comparative half-lives of these transitions allow a sensitive probe of the CVC hypothesis. Moreover, by providing the most accurate determination of V$_{ud}$, the up-down quark-mixing element, these data serve as a stringent test of the unitarity of the CKM matrix of the Standard Model. However, prior to new results, the sum of squares of the top-row CKM elements failed to meet unity by more than 2 $\sigma $. As a possible explanation for this default, uncertainties in the Coulomb corrections applied to the experimental data were pointed out. It became therefore essential to extend the study to heavy odd-odd (A $\ge $ 62) and medium mass (18 $\le $ A $\le $ 42) nuclei where these corrections are predicted to be much larger. In this context, the $\beta -\gamma $ decays of $^{62}$Ga and $^{38}$Ca have been investigated at the IGISOL and ISOLDE facilities. The results obtained will be presented. Prospects for the continuation of this work will be also discussed.