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

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 ($E_{c.m.}=60\mathrm{keV}$) 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.

Submitted to Phys. Rev. Lett

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