Measurement of the $^{14}$N(n,p)$^{14}$C cross section at the CERN n_TOF facility from sub-thermal energy to 800 keV

Background: The $^{14}$N(n,p)$^{14}$C reaction is of interest in neutron capture therapy, where nitrogen-related dose is the main component due to low-energy neutrons, and in astrophysics, where 14N acts as a neutron poison in the s-process. Several discrepancies remain between the existing data obtained in partial energy ranges: thermal energy, keV region and resonance region. Purpose: Measuring the 14N(n,p)14C cross section from thermal to the resonance region in a single measurement for the first time, including characterization of the first resonances, and providing calculations of Maxwellian averaged cross sections (MACS). Method: Time-of-flight technique. Experimental Area 2 (EAR-2) of the neutron time-of-flight (n_TOF) facility at CERN. $^{10}$B(n,${\alpha}$)$^7$Li and $^{235}$U(n,f) reactions as references. Two detection systems running simultaneously, one on-beam and another off-beam. Description of the resonances with the R-matrix code sammy. Results: The cross section has been measured from sub-thermal energy to 800 keV resolving the two first resonances (at 492.7 and 644 keV). A thermal cross-section (1.809$\pm$0.045 b) lower than the two most recent measurements by slightly more than one standard deviation, but in line with the ENDF/B-VIII.0 and JEFF-3.3 evaluations has been obtained. A 1/v energy dependence of the cross section has been confirmed up to tens of keV neutron energy. The low energy tail of the first resonance at 492.7 keV is lower than suggested by evaluated values, while the overall resonance strength agrees with evaluations. Conclusions: Our measurement has allowed to determine the $^{14}$N(n,p) cross-section over a wide energy range for the first time. We have obtained cross-sections with high accuracy (2.5 %) from sub-thermal energy to 800 keV and used these data to calculate the MACS for kT = 5 to kT = 100 keV