First Accurate Normalization of the $β$-delayed $α$ Decay of $^{16}$N and Implications for the $^{12}$C$(α,γ)^{16}$O Astrophysical Reaction Rate

Abstract

The $^{12}\text{C}(α,γ){}^{16}\text{O}$ reaction plays a central role in astrophysics, but its cross section at energies relevant for astrophysical applications is only poorly constrained by laboratory data. The reduced $α$ width, $γ_{11}$, of the bound $1^-$ level in $^{16}$O is particularly important to determine the cross section. The magnitude of $γ_{11}$ is determined via sub-Coulomb $α$-transfer reactions or the $β$-delayed $α$ decay of $^{16}$N, but the latter approach is presently hampered by the lack of sufficiently precise data on the $β$-decay branching ratios. Here we report improved branching ratios for the bound $1^-$ level [$b_{β,11} = (5.02\pm 0.10)\times 10^{-2}$] and for $β$-delayed $α$ emission [$b_{βα} = (1.59\pm 0.06)\times 10^{-5}$]. Our value for $b_{βα}$ is 33% larger than previously held, leading to a substantial increase in $γ_{11}$. Our revised value for $γ_{11}$ is in good agreement with the value obtained in $α$-transfer studies and the weighted average of the two gives a robust and precise determination of $γ_{11}$, which provides significantly improved constraints on the $^{12}$C$(α,γ)$ cross section in the energy range relevant to hydrostatic He burning.

6 pages, 5 figures