  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.
