R-Matrix Analysis of the 13C($\alpha$,n)16O Reaction

\let\s\textsuperscript The \s{13}C($\alpha$,n)\s{16}O reaction plays a crucial role in the main \emph{s}-process occurring in low-mass thermally-pulsing asymptotic giant branch (TP-AGB) stars, which produces about half of all nuclei heavier than iron. However, direct measurements of this reaction cross section near the Gamow-peak energy are currently not possible due to very small reaction cross sections. Additionally, available cross-section data at higher energy have some inconsistencies, leading to significant uncertainties in low energy extrapolations. A global R-matrix fit was conducted, using all available data for the \s{13}C($\alpha$,n)\s{16}O, \s{13}C($\alpha$,$\alpha$)\s{13}C, and \s{16}O(n,n)\s{16}O reactions. Of particular importance was the inclusion of the fixed ANC for the $1/2$+ state at $6.356$ MeV in \s{17}O, which was measured recently using the sub-Coulomb $\alpha$-transfer reaction, as well as the new \s{13}C+$\alpha$ elastic-scattering data measured in the low-energy region $1.6 - 3.8$ MeV. Important constraining information on various resonances was found, and the uncertainty for the astrophysical \s{13}C($\alpha$,n)\s{16}O reaction rate was dramatically reduced.