${}^{13}\mathrm{N}\left(p,\gamma \right){}^{14}\mathrm{O}$ is one of the key reactions which trigger the onset of the hot CNO cycle. This transition occurs when the proton capture rate on ${}^{13}\mathrm{N}$ is faster, due to increasing stellar temperature $\left(⩾{10}^8\mathrm{K}\right)$, than the ${}^{13}\mathrm{N}$ $\beta$-decay rate. The rate of this reaction is dominated by the resonant capture through the first excited state of ${}^{14}\mathrm{O}$ $\left(E_r=0.528\text{MeV}\right)$. However, through constructive interference, direct capture below the resonance makes a non-negligible contribution to the reaction rate. We have determined this direct contribution by measuring the asymptotic normalization coefficient for ${}^{14}\mathrm{O}\to {}^{13}\mathrm{N}+p$. In our experiment, an $11.8\text{MeV}∕\text{nucleon}$ ${}^{13}\mathrm{N}$ radioactive beam was used to study the ${}^{14}\mathrm{N}\left({}^{13}\mathrm{N},{}^{14}\mathrm{O}\right){}^{13}\mathrm{C}$ peripheral transfer reaction, and the asymptotic normalization coefficient, ${\left(C_{p_{1∕2}}^{{}^{14}\mathrm{O}}\right)}^2=29.0\pm 4.3{\text{fm}}^{-1}$, was extracted from the measured cross section. The radiative capture cross section was estimated using an $R$-matrix approach with the measured asymptotic normalization coefficient and the latest resonance parameters. We find the $S$ factor for ${}^{13}\mathrm{N}\left(p,\gamma \right){}^{14}\mathrm{O}$ to be larger than previous estimates. Consequently, the transition from the cold to hot CNO cycle for novae would be controlled by the slowest proton capture reaction ${}^{14}\mathrm{N}\left(p,\gamma \right){}^{15}\mathrm{O}$.

• Received 29 October 2003

DOI:https://doi.org/10.1103/PhysRevC.69.055807