Shell-model half-lives including first-forbidden contributions for r -process waiting-point nuclei

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We have performed large-scale shell-model calculations of the half-lives and neutron-branching probabilities of the r-process waiting-point nuclei at the magic neutron numbers $N=50$, 82, and 126. The calculations include contributions from allowed Gamow-Teller and first-forbidden transitions. We find good agreement with the measured half-lives for the $N=50$ nuclei with charge numbers $Z=28$--32 and for the $N=82$ nuclei ¹²⁹Ag and ¹³⁰Cd. The contribution of forbidden transitions reduce the half-lives of the $N=126$ waiting-point nuclei significantly, while they have only a small effect on the half-lives of the $N=50$ and 82 r-process nuclei.