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

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