$\beta$ -decay half-lives of neutron-rich nuclei around $N=82$ are key data to understand the $r$-process nucleosynthesis. We performed large-scale shell-model calculations in this region using a newly constructed shell-model Hamiltonian, and successfully described the low-lying spectra and half-lives of neutron-rich $N=82$ and $N=81$ isotones with $Z=42\text{--}49$ in a unified way. We found that their Gamow–Teller strength distributions have a peak in the low excitation energies, which significantly contributes to the half-lives. This peak, dominated by $\nu 0g_{7/2} \to \pi 0g_{9/2}$ transitions, is enhanced on the proton-deficient side because the Pauli-blocking effect caused by occupying the valence proton $0g_{9/2}$ orbit is weakened.

中文翻译：

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壳模型计算富中子 N = 82,81 原子核的 Gamow-Teller 跃迁

$\beta$ - 富中子核在 $N=82$ 附近的衰变半衰期是理解 $r$ 过程核合成的关键数据。我们使用新构建的壳模型哈密顿量在该区域进行了大规模壳模型计算，并成功地描述了富含中子的 $N=82$ 和 $N=81$ 同位素的低位光谱和半衰期$Z=42\text{--}49$ 统一。我们发现他们的 Gamow-Teller 强度分布在低激发能中有一个峰值，这对半衰期有很大贡献。这个由 $\nu 0g_{7/2} \到 \pi 0g_{9/2}$ 跃迁支配的峰在质子缺乏侧得到增强，因为占据价质子 $0g_{ 9/2}$轨道减弱。