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

TL;DR

This study provides a refined measurement of the $^{13}$C(p,$$N) reaction's $S$-factor at energies relevant to stellar processes, improving the understanding of nucleosynthesis in stars and the chemical evolution of the Galaxy.

Contribution

The paper presents new experimental data, resonance parameters, and an updated reaction rate for the $^{13}$C(p,$$N) reaction, enhancing previous models and measurements.

Findings

$S$-factor results are about 20% lower than previous data.

New resonance strength for the 7966.9 keV state is reported as 18(2) meV.

Updated reaction rate and parameters for stellar nucleosynthesis models.

Abstract

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, $S_{\mathrm{tot}}$(0) = 6.4(4) keV b. Finally a new reaction rate is calculated and reported here.