Shell-model half-lives including first-forbidden contributions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>r</mml:mi></mml:math>-process waiting-point nuclei

Abstract

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 ${}^{129}$Ag and ${}^{130}$Cd. 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.