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 $E_{mathrm{c.m.}}$ = 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$_mathrm{g.s.}$ $rightarrow$ $^{12}$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 ($sim$two orders of magnitude) densities than initially predicted.
Angular distribution of the 12C(7Li,6He)13N reaction at E(7Li) = 44.0 MeV was measured at the HI-13 tandem accelerator of Beijing, China. Asymptotic normalization coefficient (ANC) of 13N = 12C + p was derived to be 1.64 $pm$ 0.11 fm$^{-1/2}$ through
distorted wave Born approximation (DWBA) analysis. The ANC was then used to deduce the astrophysical $S(E)$ factors and reaction rates for direct capture in 12C(p,g)13N at energies of astrophysical relevance.
