Improved $S$-factor of the ${}^{13}$C(p,$\gamma$)${}^{14}$N reaction at $E_{\mathrm{p}}=$330-740 keV and parameters of resonances at 448 keV and 551 keV

The ${}^{13}$C(p,$\gamma$)${}^{14}$N reaction is the second reaction of the CNO cycle. This cycle takes place in our Sun and fuels massive, Red, and Asymptotic Giant Branch stars. The ${}^{13}$C(p,$\gamma$)${}^{14}$N rate affects the final abundances of ${}^{12,13}$C and ${}^{19}$F nuclides, with impact on our understanding of the i- and s-process, giant star nucleosynthesis and mixing processes, and ultimately the chemical evolution of the Galaxy. Here, we report on a new measurement of the ${}^{13}$C(p,$\gamma$)${}^{14}$N cross-section, which has been performed at the Felsenkeller shallow-underground laboratory in Dresden (Germany). The present $S$-factor results agree at low energy with LUNA data but are about 20% lower than previous literature data over the whole energy range explored, $E=$310-680 keV. The narrow resonance corresponding to the 7966.9(5) keV excited state has been investigated and we report a new resonance strength, $\omega \gamma =$18(2) meV. In addition a new R-matrix fit is presented, from which new parameters for the broad resonance corresponding to the 8062.0(10) keV excited state are derived and a new extrapolation for the total $S$-factor down to zero energy is obtained, $S_{\mathrm{t}\mathrm{o}\mathrm{t}}$(0) = 6.4(4) keV b. Finally a new reaction rate is calculated and reported here.