$S$ factor of $^{13}$C($α$,$n$)$^{16}$O at low energies in cluster effective field theory

The $^{13}$C($α$,$n$)$^{16}$O reaction at low energies is studied by constructing an effective field theory. We choose a separation scale at $E=1$~MeV, where $E$ is the initial $α$-$^{13}$C energy in center-of-mass frame, just below the sharp resonant $5/2^+$ state of $^{17}$O, and include two open