New proton-capture rates on carbon isotopes and their impact on the astrophysical $^{12}\mathrm{C}/{}^{13}\mathrm{C}$ ratio

TL;DR

This study provides the most precise measurements of proton-capture rates on carbon isotopes, significantly impacting the understanding of the $^{12}$C/$^{13}$C ratio in stellar nucleosynthesis and mixing processes.

Contribution

It offers new, highly precise reaction rates at energies relevant to stellar environments, revising previous values and refining models of stellar nucleosynthesis.

Findings

Reaction rates are systematically lower than previous data.

The lowest $^{12}$C/$^{13}$C ratio during H burning is now estimated at 3.6 ± 0.4.

Provides reaction data at energies down to 60 keV, relevant for giant star shells.

Abstract

The ${}^{12}\mathrm{C}/{}^{13}\mathrm{C}$ ratio is a significant indicator of nucleosynthesis and mixing processes during hydrogen burning in stars. Its value mainly depends on the relative rates of the ${}^{12}\mathrm{C}(p,\gamma){}^{13}\mathrm{N}$ and ${}^{13}\mathrm{C}(p,\gamma){}^{14}\mathrm{N}$ reactions. Both reactions have been studied at the Laboratory for Underground Nuclear Astrophysics (LUNA) in Italy down to the lowest energies to date ($E_\mathrm{c.m.} = 60\,\mathrm{keV}$) reaching for the first time the high energy tail of hydrogen burning in the shell of giant stars. Our cross sections, obtained with both prompt $\gamma$-ray detection and activation measurements, are the most precise to date with overall systematic uncertainties of $7-8\%$. Compared with most of the literature, our results are systematically lower, by $25\%$ for the ${}^{12}\mathrm{C}(p,\gamma){}^{13}\mathrm{N}$ reaction and by $30\%$ for ${}^{13}\mathrm{C}(p,\gamma){}^{14}\mathrm{N}$. We provide the most precise value up to now of $(3.6 \pm 0.4)$ in the $20-140\,\mathrm{MK}$ range for the lowest possible ${}^{12}\mathrm{C}/{}^{13}\mathrm{C}$ ratio that can be produced during H burning in giant stars.