Summary

In summary, the isospin- and angular-momentum-projected DFT theory has been employed to calculate isospin mixing and isospin-breaking corrections to the $0^+\rightarrow 0^+$ Fermi superallowed $\beta$-decay. Our parameter-free model capitalizes on the ability of the MF approach to describe long-range polarization effects. The self-consistent HF wave functions containing essential correlations due to the symmetry-breaking mechanism are then used as trial states during the projection procedure. The results for $\alpha_C$ in $^{80}$Zr are consistent with current experimental estimates from the giant dipole resonance studies. The preliminary results on the $\delta_C$-corrections are also very encouraging. The calculated values of the nucleus-independent $\bar{{\cal F}t}= 3069.4(10)$ and the $V_{\mbox{\scriptsize {ud}}} = 0.97463(24)$ are consistent with the recent evaluations of Ref. [7].

This work was supported in part by the Polish Ministry of Science under Contracts numbers N N202 328234 and N N202 239037, Academy of Finland and University of Jyväskylä within the FIDIPRO programme, and by the Office of Nuclear Physics, U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee) and DE-FC02-09ER41583 (UNEDF SciDAC Collaboration). We acknowledge the CSC - IT Center for Science Ltd, Finland for the allocation of computational resources.