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

Gamow-Teller transitions of neutron-rich $N=82,81$ nuclei by shell-model calculations