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The $^{12}\text{C}(\alpha,\gamma){}^{16}\text{O}$ reaction plays a centralrole in astrophysics, but its cross section at energies relevant forastrophysical applications is only poorly constrained by laboratory data. Thereduced $\alpha$ width, $\gamma_{11}$, of the bound $1^-$ level in $^{16}$O isparticularly 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 ispresently hampered by the lack of sufficiently precise data on the$\beta$-decay branching ratios. Here we report improved branching ratios forthe bound $1^-$ level [$b_{\beta,11} = (5.02\pm 0.10)\times 10^{-2}$] and for$\beta$-delayed $\alpha$ emission [$b_{\beta\alpha} = (1.59\pm 0.06)\times10^{-5}$]. 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 $\alpha$-transferstudies and the weighted average of the two gives a robust and precisedetermination of $\gamma_{11}$, which provides significantly improvedconstraints on the $^{12}$C$(\alpha,\gamma)$ cross section in the energy rangerelevant to hydrostatic He burning.

physical review letters

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