The evolution of massive stars with very low-metallicities depends critically on the amount of CNO nuclides which they produce. The ${}^{12}$N($p,\gamma$)${}^{13}$O reaction is an important branching point in the rap processes, which are believed to be alternative paths to the slow $3\alpha$ process for producing CNO seed nuclei and thus could change the fate of massive stars. In the present work, the angular distribution of the ${}^2$H(${}^{12}$N, ${}^{13}$O)$n$ proton transfer reaction at $E_{\mathrm{c}.\mathrm{m}.}=8.4$ MeV has been measured for the first time. Based on the Johnson-Soper approach, the square of the asymptotic normalization coefficient (ANC) for the virtual decay of ${}^{13}$O${}_{\mathrm{g}}.\mathrm{s}.$ $\to$ ${}^{12}$N+$p$ was extracted to be $3.92\pm 1.47$ fm${}^{-1}$ from the measured angular distribution and utilized to compute the direct component in the ${}^{12}$N($p,\gamma$)${}^{13}$O reaction. The direct astrophysical $S$ factor at zero energy was then found to be $0.39\pm 0.15$ keV b. By considering the direct capture into the ground state of ${}^{13}$O, the resonant capture via the first excited state of ${}^{13}$O and their interference, we determined the total astrophysical $S$ factors and rates of the ${}^{12}$N($p,\gamma$)${}^{13}$O reaction. The new rate is two orders of magnitude slower than that from the REACLIB compilation. Our reaction network calculations with the present rate imply that ${}^{12}$N($p,\gamma$)${}^{13}$O will only compete successfully with the ${\beta }^{+}$ decay of ${}^{12}$N at higher ($\sim 2$ orders of magnitude) densities than initially predicted.

• Received 14 May 2012

DOI:https://doi.org/10.1103/PhysRevC.87.015803