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

Abstract

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 [$b_{\beta,11} = (5.02\pm 0.10)\times 10^{-2}$] and for $\beta$-delayed $\alpha$ emission [$b_{\beta\alpha} = (1.59\pm 0.06)\times 10^{-5}$]. Our value for $b_{\beta\alpha}$ 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.