Multichannel study of the C13(α,n)O16 and O16(n,γ)O17 reactions

The $^{13}\mathrm{C}(\ensuremath{\alpha},n)^{16}\mathrm{O}$ reaction is investigated in a microscopic two-cluster model with an effective interaction recently developed for transfer reactions. The wave functions are defined in the generator coordinate method. The basis includes all $^{13}\mathrm{C}$+\ensuremath{\alpha} and $^{16}\mathrm{O}$+n channels with $^{13}\mathrm{C}$ and $^{16}\mathrm{O}$ described in the p shell. Particle-hole excitations in the sd shell are also taken into account in order to include the $^{16}\mathrm{O}$$({3}^{\ensuremath{-}})$+n channel. The $^{17}\mathrm{O}$ spectroscopy is in good agreement with experiment. In particular, the width of the astrophysically relevant $1/{2}_{2}^{+}$ state is well reproduced ($\ensuremath{\Gamma}=121\phantom{\rule{0.3em}{0ex}}\text{keV}$ as compared to the experimental value $\ensuremath{\Gamma}=124\ifmmode\pm\else\textpm\fi{}12\phantom{\rule{0.3em}{0ex}}\text{keV}$). The calculation of the $^{13}\mathrm{C}(\ensuremath{\alpha},n)^{16}\mathrm{O}$ S factor shows the importance of the $3/{2}_{3}^{+}$ resonance, and provides $S(0.2\phantom{\rule{0.3em}{0ex}}\mathrm{MeV})=2.1\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}\text{MeV}$ b, slightly lower than the NACRE recommended value ($2.5\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}\text{MeV}$ b). The same model is applied to the $^{16}\mathrm{O}(n,\ensuremath{\gamma})^{17}\mathrm{O}$ radiative-capture reaction at thermal and astrophysical energies.