Improved $S$-factor of the $^{12}$C(p,$\gamma$)$^{13}$N reaction at $E\,=\,$320-620~keV and the 422~keV resonance

The 12C(p,{\gamma})13N reaction is the onset process of both the CNO and Hot CNO cycles that drive massive star, Red and Asymptotic Giant Branch star and novae nucleosynthesis. The 12C(p,{\gamma})13N rate affects the final abundances of the stable 12,13C nuclides, with ramifications for meteoritic carbon isotopic abundances and the s-process neutron source strength. Here, a new underground measurement of the 12C(p,{\gamma})13N cross-section is reported. The present data, obtained at the Felsenkeller shallow-underground laboratory in Dresden (Germany), encompass the 320-620 keV center of mass energy range to include the wide and poorly constrained E = 422 keV resonance that dominates the rate at high temperatures. This work S-factor results, lower than literature by 25%, are included in a new comprehensive R-matrix fit, and the energy of the 1+ first excited state of 13N is found to be 2369.6(4) keV, with radiative and proton width of 0.49(3) eV and 34.9(2) keV respectively. A new reaction rate, based on present R-matrix fit and extrapolation, is suggested.