Isospin mixing in nuclei around $N\simeq Z$ and the superallowed $\beta$-decay

W. Satula, J. Dobaczewski, W. Nazarewicz, and M. Rafalski

Abstract:

Theoretical approaches that use one-body densities as dynamical variables, such as Hartree-Fock or the density functional theory (DFT), break isospin symmetry both explicitly, by virtue of charge-dependent interactions, and spontaneously. To restore the spontaneously broken isospin symmetry, we implemented the isospin-projection scheme on top of the Skyrme-DFT approach. This development allows for consistent treatment of isospin mixing in both ground and exited nuclear states. In this study, we apply this method to evaluate the isospin impurities in ground states of even-even and odd-odd $N\simeq Z$ nuclei. By including simultaneous isospin and angular-momentum projection, we compute the isospin-breaking corrections to the $0^+\rightarrow 0^+$ superallowed $\beta$-decay.