Sensitivity of the C13(α,n)O16S factor to the uncertainty in the level parameters of the near-threshold state

Abstract

The $^{13}\mathrm{C}(\ensuremath{\alpha},n)^{16}\mathrm{O}$ reaction is the main source of neutrons for the $s$ and $i$ processes in asymptotic giant branch stars and carbon-enhanced metal-poor stars, respectively. The reaction rate over the relevant temperature range from 0.1 to 0.3 GK translates into a center-of-mass energy range of 150 to 540 keV. Current measurements extend down to 300 keV, still requiring an extrapolation of the cross section. At these low energies, the high-energy tail of a $1/{2}^{+}$ state near the reaction threshold makes a significant contribution to the cross section, but its amplitude is still highly uncertain. In this paper the uncertainties associated with the low-energy cross-section extrapolation are investigated, in particular the sensitivity to the energy, width, and Coulomb renormalized asymptotic normalization coefficient of the near-threshold resonance. Recently it has been suggested that the energy of the near-threshold level may have a large impact on the extrapolation, but this is not found to be the case compared with the other sources of uncertainty.