Summary

We presented a novel no-core configuration-interaction approach, which is based on mixing the isospin- and angular-momentum-projected deformed DFT configurations. The model is specifically tailored to determining the low-lying spectra and $\beta$-decay transitions in $N\approx Z$ nuclei, where the isospin degree of freedom is essential. The model can be viewed as a variant of the no-core shell model. Its advantage over the standard shell model formulation is that it can be applied, at least in principle, to any nucleus of arbitrary mass and number parity.

Two applications of the model, both relevant to studies of superallowed Fermi $\beta$ decays, were presented. The model has been used to compute the $0^+$ spectrum of $^{62}$Zn and ISB corrections to the Fermi $\beta$ decays between the $0_1^+\rightarrow 0_1^+$ and $0_2^+\rightarrow 0_2^+$ isobaric analogue states in $^{38}$Ca and $^{38}$K. We demonstrated that without adjusting any single parameter, it well reproduces the spectra of $0^+$ states. Predictions for the ISB corrections appear to be, at least at present, somewhat less reliable. The reason is that the isospin mixing is a very subtle effect, requiring a perfect matching of spaces of states used in the parent and daughter nuclei, which is difficult to achieve in practice. Work toward improving this aspect of the model is in progress.

This work was supported in part by the Polish National Science Centre (NCN) under Contract No. 2012/07/B/ST2/03907, by the THEXO JRA within the EU-FP7-IA project ENSAR (No. 262010), by the ERANET-NuPNET grant SARFEN of the Polish National Centre for Research and Development (NCBiR), and by the Academy of Finland and University of Jyväskylä within the FIDIPRO programme.