Numerical results

The CKM matrix element $\vert V_{ud}\vert=0.97397(27)$ obtained with a set of the ISB corrections calculated using the double-projected DFT method [4] agrees very well with the result obtained by Towner and Hardy (TH) [11], $\vert V_{ud}\vert=0.97418(26)$, obtained within methodology based on the nuclear shell-model combined with Woods-Saxon mean-field (SM+WS) wave functions. Both values result in the unitarity of the CKM matrix up to 0.1%. It is gratifying to see that also individual DFT values of $\delta_{\rm C}$ are consistent within 2$\sigma$ with the values calculated in Ref. [11] (see Fig. 7 of Ref. [4]). This holds up to three exceptions of the ISB corrections to $^{10}$C$\rightarrow$$^{10}$B, $^{38}$K$\rightarrow$$^{38}$Ar, and $^{62}$Ga$\rightarrow$$^{62}$Zn transitions. The two latter mass numbers, more precisely transitions $^{38}$Ca$\rightarrow$$^{38}$K and $^{62}$Ga$\rightarrow$$^{62}$Zn, are analyzed below using the newly developed NCCI approach. It is worth mentioning here that the mutually consistent DFT and TH results are at variance with the RPA-based study of Ref. [12], which gives systematically smaller values of $\delta_{\rm C}$ and, in turn, considerably smaller value of matrix element $V_{ud}$.