We perform large-scale shell-model calculations of $\beta$-decay properties for neutron-rich nuclei with $13\le Z\le 18$ and $22\le N\le 34$, taking the first-forbidden transitions into account. The natural-parity and unnatural-parity states are calculated in the $0\hslash \omega$ and $1\hslash \omega$ model spaces, respectively, within the full $sd+pf+sdg$ valence shell. The calculated $\beta$-decay half-lives and $\beta$-delayed neutron emission probabilities show good agreement with the experimental data. The first-forbidden transitions make a non-negligible contribution to the half-lives of $N\gtrsim 28$ nuclei. The low-lying Gamow-Teller strengths of even-even nuclei are considerably larger than those of the neighboring odd-$A$ and odd-odd nuclei, strongly affecting the half-lives and neutron emission probabilities. It is shown that this even-odd effect is caused by the $J^{\pi }=1^{+}$ proton-neutron pairing interaction. We derive a formula to represent the positions of the Gamow-Teller giant resonances from the calculated strength distributions.

• Received 13 March 2018

DOI:https://doi.org/10.1103/PhysRevC.97.054321