Ab initio study of $\beta$-decay and pairing in $N=Z$ nuclei

Abstract

We investigate the $\beta$-decay properties of $rp$-process waiting-point nuclei ${}^{72}$Kr, ${}^{68}$Se, and ${}^{64}$Ge from realistic nuclear forces based on chiral effective field theory. The \textit{ab initio} valence-space in-medium similarity renormalization group method is employed for this purpose to consistently derive Hamiltonians and Gamow-Teller operators from chiral two- and three-nucleon interactions. The calculated half-lives and branching ratios indicate that nearly the entire decay intensity is confined within 1 MeV of excitation energy in the daughter nuclei. We address the isoscalar and isovector pairing and their impact on ground state properties of these waiting-point nuclei, along with several other $N=Z$ systems in the $fp$-shell. Our results do not provide evidence for an isoscalar condensate or any dominant isovector pairing condensate-like phase in these $N=Z$ nuclei. We present the full $B(\mathrm{GT})$ strength distributions and discuss the influence of pairing correlations on them. The present work provides a microscopic picture of $\beta$-decay strengths and pairing in $N=Z$ nuclei far from the stability line.

10 pages, 5 figures

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