Nuclear $\beta^-$-decay half-lives for $fp$ and $f_{5/2}pg_{9/2}$ shell nuclei
In the present work we calculate the allowed $\beta^-$-decay half-lives of nuclei with $Z = 20 -30$ and N $\leq$ 50 systematically under the framework of the nuclear shell model. A recent study shows that some nuclei in this region belonging to the island of inversion. We perform calculation for $fp$ shell nuclei using KB3G effective interaction. In the case of Ni, Cu, and Zn, we used JUN45 effective interaction. Theoretical results of $Q$ values, half-lives, excitation energies, log$ft$ values, and branching fractions are discussed and compared with experimental data. In Ni region, we also compared our calculated results with recent experimental data [Z. Y. Xu {\it et al.}, \emph{Phys. Rev. Lett.} \textbf{113}, 032505, 2014]. Present results showing good agreement with experimental value of half-lives in comparison to QRPA.