First Accurate Normalization of the ${\hat{I}}^2$-delayed $\hat{I}\pm$ Decay of ${}^{16}$N and Implications for the ${}^{12}$C$(\hat{I}\pm ,{\hat{I}}^3{)}^{16}$O Astrophysical Reaction Rate

Abstract

The ${}^{12}\text{C}(\hat{I}\pm ,{\hat{I}}^3){}^{16}\text{O}$ 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 $\hat{I}\pm$ width, ${\hat{I}}_{11}^3$, of the bound $1^{-}$ level in ${}^{16}$O is particularly important to determine the cross section. The magnitude of ${\hat{I}}_{11}^3$ is determined via sub-Coulomb $\hat{I}\pm$-transfer reactions or the ${\hat{I}}^2$-delayed $\hat{I}\pm$ decay of ${}^{16}$N, but the latter approach is presently hampered by the lack of sufficiently precise data on the ${\hat{I}}^2$-decay branching ratios. Here we report improved branching ratios for the bound $1^{-}$ level [$b_{{\hat{I}}^2,11}=(5.02\pm 0.10)\times 10^{-2}$] and for ${\hat{I}}^2$-delayed $\hat{I}\pm$ emission [$b_{{\hat{I}}^2\hat{I}\pm }=(1.59\pm 0.06)\times 10^{-5}$]. Our value for $b_{{\hat{I}}^2\hat{I}\pm }$ is 33% larger than previously held, leading to a substantial increase in ${\hat{I}}_{11}^3$. Our revised value for ${\hat{I}}_{11}^3$ is in good agreement with the value obtained in $\hat{I}\pm$-transfer studies and the weighted average of the two gives a robust and precise determination of ${\hat{I}}_{11}^3$, which provides significantly improved constraints on the ${}^{12}$C$(\hat{I}\pm ,{\hat{I}}^3)$ cross section in the energy range relevant to hydrostatic He burning.

6 pages, 5 figures