The ${}^{13}\mathrm{C}$($\alpha ,n$)${}^{16}\mathrm{O}$ 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 α 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.

• Received 31 May 2007

DOI:https://doi.org/10.1103/PhysRevC.77.042801