Isospin mixing in the vicinity of the $N=Z$ line

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

Abstract:

We present the isospin- and angular-momentum-projected nuclear density functional theory (DFT) and its applications to the isospin-breaking corrections to the superallowed $\beta$-decay rates in the vicinity of the $N=Z$ line. A preliminary value obtained for the Cabbibo-Kobayashi-Maskawa matrix element, $\vert V_{ud}\vert= 0.97463(24)$, agrees well with the recent estimate by Towner and Hardy [Phys. Rev. C77, 025501 (2008)]. We also discuss new opportunities to study the symmetry energy by using the isospin-projected DFT.