AstrophysicalSfactorfor 13C(p,γ)14Nand asymptotic normalization coefficients

Abstract

We reanalyze the ${}^{13}\mathrm{C}(p,\ensuremath{\gamma}{)}^{14}\mathrm{N}$ radiative capture reaction within the R-matrix approach. The low-energy astrophysical S factor has important contributions from both resonant and onresonant captures. The normalization of the nonresonant component of the transition to a particular ${}^{14}\mathrm{N}$ bound state is expressed in terms of the asymptotic normalization coefficient (ANC). In the analysis we use the experimental ANC's inferred from $\mathrm{the}{}^{13}\mathrm{C}{(}^{14}\mathrm{N}{,}^{13}\mathrm{C}{)}^{14}\mathrm{N}$ and ${}^{13}\mathrm{C}{(}^{3}\mathrm{He}{,d)}^{14}\mathrm{N}$ reactions. The fits of the calculated S factors to the experimental data are sensitive to the ANC values and are used to test the extracted ANC's. We find that for transitions to all the states $\mathrm{in}{}^{14}\mathrm{N},$ except the third excited state, the ANC's determined from the transfer reactions provide the best fit. The astrophysical factor we obtain, $S(0)=7.7\ifmmode\pm\else\textpm\fi{}1.1 \mathrm{keV}\mathrm{}\mathrm{b},$ is in excellent agreement with previous results.