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

The ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ 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 ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ rate affects the final abundances of the stable ${}^{12,13}\mathrm{C}$ nuclides with ramifications for meteoritic carbon isotopic abundances and the $s$-process neutron source strength. Here, an underground measurement of the ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ 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 $S$-factor results, lower than literature by 25%, are included in a comprehensive $R$-matrix fit, and the energy of the ${\frac{1}{2}}^{+}$ first excited state of ${}^{13}\mathrm{N}$ is found to be 2369.6(4) keV with a radiative and proton width of 0.49(3) eV and 34.9(2) keV, respectively. A reaction rate, based on the present $R$-matrix fit and extrapolation, is suggested.

Figure 1

Schematic top view of the present setup. The detector main features are summarized in Table 1. Not to scale.

Figure 2

The $\gamma$-ray spectra acquired at $E_p=464$ keV, top, and at 670 keV, bottom. The $\gamma$ ray from the ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ reaction is labeled in red. The typical environmental and beam induced background $\gamma$ rays are indicated.

Figure 3

Comparison between yields from detectors B (${114}^{\circ }$), C (${22}^{\circ }$), D (${122}^{\circ }$), and E (${55}^{\circ }$) at three different beam energies. The data confirm that the $\gamma$ ray of interest is isotropic as expected. Detector C was removed for technical reasons and replaced in a different position before runs at $E_p=400$ and 465 keV without reperforming a proper efficiency calibration, thus these data are not included. The $x$-axis error bars include the contribution from the detector position uncertainty ($2^{\circ }$) and the opening angle of the detector ($8^{\circ }$ for C and $5^{\circ }$ for detectors B and D).

Figure 4

Present results for the ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ reaction $S\left(E\right)$, red points, compared with data available in literature. The present $R$-matrix fit is shown in black and compared with the similar fit reported in [20], blue line.

Figure 5

The astrophysical reaction rate from the present work (red), normalized to NACRE [43]. The uncertainty of the present rate is within 9% over the entire temperature range. The reaction rate in [42], normalized to NACRE, is reported for comparison.