Determination of theC12+presonance energy at 14.2 MeV

The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+$p$ resonance energy of the lowest $T=\frac{3}{2}$ state in ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ has been determined by using the 100 cm broad-range magnetic spectrograph to measure the incident proton beam energy and a solid state detector to measure the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p, p){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ yield curve. Phase-shift analyses of 10 proton elastic scattering yield curves taken at a laboratory observation angle of 160° give a value of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+ $p$ resonance energy of 14.2325±0.0022 MeV. We compare our result with that of a recent time-of-flight measurement (14.230 75 ± 0.000 20 MeV) and conclude that the nuclear-reaction energy scale based on the ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}\left(\alpha \right)$ energy is in agreement with the absolute measurement against the meter and second to within an uncertainty of better than 0.016%.