Constraint of the $^{13}$C($\alpha$,n) Cross Section Toward Astrophysical Energies for the Main s-Process

The slow neutron capture process (s-process) typically occurs in relatively low neutron flux environments, such as AGB stars, and is a key mechanism in heavy-element synthesis. The dominant source of neutrons for the main s-process is the $^{13}$C($\alpha$,n) reaction, which proceeds at stellar temperatures ($\sim 0.1$GK, 200 keV), via reactions well below the Coulomb barrier. Direct measurements of the reaction rate in the Gamow window ($\sim 140-230$ keV) is difficult, complicated by the low yields and high beam currents required. Current measurements have constrained the cross section down to approximately 320 keV - still well above stellar conditions- with significant statistical uncertainties. These uncertainties, and the influence of a near-threshold $1/2^+$ state at 6.4 MeV, means that extrapolation of the data into the Gamow window is unreliable. These measurements typically use high-efficiency moderated neutron counter detectors, meaning energy information of the incident neutrons is lost. A quasi-spectroscopic approach has been used to measure the $^{13}$C($\alpha$,n) reaction rate at energies between 300-350 keV with the aim of reducing uncertainties in current measurements.