Systematic shell-model study of β -decay properties and Gamow-Teller strength distributions in A≈40 neutron-rich nuclei

Abstract

We perform large-scale shell-model calculations of $\ensuremath{\beta}$-decay properties for neutron-rich nuclei with $13\ensuremath{\le}Z\ensuremath{\le}18$ and $22\ensuremath{\le}N\ensuremath{\le}34$, taking the first-forbidden transitions into account. The natural-parity and unnatural-parity states are calculated in the $0\ensuremath{\hbar}\ensuremath{\omega}$ and $1\ensuremath{\hbar}\ensuremath{\omega}$ model spaces, respectively, within the full $sd+pf+sdg$ valence shell. The calculated $\ensuremath{\beta}$-decay half-lives and $\ensuremath{\beta}$-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 $N\ensuremath{\gtrsim}28$ 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 ${J}^{\ensuremath{\pi}}={1}^{+}$ proton-neutron pairing interaction. We derive a formula to represent the positions of the Gamow-Teller giant resonances from the calculated strength distributions.