Indirect study of the C 13 ( α , n ) O 16 reaction via the C 13 ( Li 7 , t ) O 17 transfer reaction

The $^{13}\mathrm{C}$($\ensuremath{\alpha},n$)$^{16}\mathrm{O}$ reaction is considered the main neutron source for the s process in low mass asymptotic giant branch (AGB) stars. In the Gamow peak, the cross section sensitively depends on the $1/{2}^{+}$ subthreshold state of $^{17}\mathrm{O}$ (${E}_{x}=6.356$ MeV). In this work, we determined the astrophysical $S$ factor through an evaluation of the \ensuremath{\alpha} spectroscopic factor and the corresponding asymptotic normalization factor (ANC) of the 6.356 MeV state using the transfer reaction $^{13}\mathrm{C}$($^{7}\mathrm{Li}$,$t$)$^{17}\mathrm{O}$ at two different incident energies. Our result confirms that the contribution of the $1/{2}^{+}$ state is dominant at astrophysical energies. Our reaction rate at $T=0.09$ GK is slightly lower than the value adopted in the Nuclear Astrophysics Compilation of REaction rates (NACRE), but two times larger than the one obtained in a recent ANC measurement.