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

TL;DR

This work delivers a high-precision measurement of the 13C(p,gamma)14N cross-section in the 310–680 keV range using the Felsenkeller facility, and performs a comprehensive R-matrix analysis to extract resonance parameters for the narrow 448.5 keV and broad 551 keV states. The study finds a reduced S-factor compared with previous literature (about 20% lower) and reports a resonance strength ωγ = 18(2) meV for the 448.5 keV state, along with a refined S_tot(0) = 6.4(4) keV b and updated broad-resonance parameters. The resulting astrophysical reaction rate is about 7% uncertain and typically lower than NACRE, impacting CNO-cycle nucleosynthesis and fluorine production in AGB stars, and aligning with recent LUNA results at low energies. Overall, the improved data and analysis provide tighter constraints on stellar models and Galactic chemical evolution related to carbon, nitrogen, and fluorine abundances.

Abstract

The $^{13}$C(p,$γ$)$^{14}$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,$γ$)$^{14}$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,$γ$)$^{14}$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, $ωγ\,=\,$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.

Figures (6)

• Figure 1: Schematic top view of the present setup (not to scale). The detector main features are in Tab. \ref{['tab:table2']}. Detector A was positioned in close, middle and far geometry for the cross-section, the broad resonance and the angular distribution investigation, respectively.
• Figure 2: Top: The $E$p$\,=\,$448.5keV resonance scan fit with target 1, blue dots and red solid line. The direct capture and tail of the broad resonance yield was calculated with eq. \ref{['eq_1']} and R-matrix curve from Ref.Skowronski-2023 is shown by dashed black line. Bottom: A comparison between the target profile obtained via peak-shape analysis at the resonance energy, green solid line and via 448.5 keV resonance scan (after subtraction of the direct capture and broad resonance contribution), red dashed line. Both profile are normalized to 1 for clarity. The target thickness is 18.4(4) keV and 18.7(4) keV from peak-shape and resonance analysis, respectively.
• Figure 3: The $\gamma$-ray spectrum acquired at $E$p = 555 keV ($E\,=\,$515 keV) with detector A in close geometry. The main $\gamma$-rays from the $^{13}$C(p,$\gamma$)$^{14}$N reaction are shown with black dashed lines. Other prominent peaks not marked are the escape peaks and the annihilation peak.
• Figure 4: The observed angular distributions, black dots, for different $^{13}$C($p,\gamma$)$^{14}$N transitions compared with extrapolation by Ref. chakraborty2015 of experimental data reported in Ref. king, dashed line. The angle $\theta$ is in the laboratory frame. As reported in Ref. king near $E$p$\,=\,$550 keV the anisotropies are compatible with unity. At energies far from the broad resonance, only the transition to 4915keV and 5691keV states show a non isotropic distribution, as found by Ref. king and as predicted by the direct capture model in Ref. rolfs. The plotted uncertainty was calculated as the sum in quadrature of statistical (1$-$2%) and the propagation of the efficiency uncertainty (6.5%).
• Figure 5: The result of the R-matrix fit, black line, of the $^{13}$C($p,\gamma$)$^{14}$N reaction cross section data available in literature Skowronski-2023kinggenardvoglhesterzeps1995. The black shaded areas show $1\sigma$, $2\sigma$ and $3\sigma$ uncertainties. The data in green for the transitions to the excited states and the total $S$-factor are from Ref. Skowronski-PhD.