Folding model approach to the elastic $p+^{12,13}$C scattering at low energies and radiative capture $^{12,13}$C$(p,\gamma)$ reactions

TL;DR

This study employs a folding model to analyze low-energy elastic proton scattering and radiative capture reactions involving carbon isotopes, providing a consistent approach that accurately reproduces experimental data and astrophysical S factors.

Contribution

It introduces a unified folding model for both scattering and capture processes, improving the theoretical description of proton interactions with carbon isotopes at astrophysical energies.

Findings

Folded optical potentials match elastic scattering data.

Calculated astrophysical S factors agree with experimental results.

Model provides a consistent framework for scattering and capture reactions.

Abstract

The proton radiative capture $^{12,13}$C$(p,{\gamma})$ reactions at astrophysical energies, key processes in the CNO cycle, are revisited in the potential model with the proton-nucleus potential for both the scattering and bound states obtained in the folding model, using a realistic density dependent nucleon-nucleon interaction. For the consistency, this same folding model is also used to calculate the optical potential of the elastic $p+^{12,13}$C scattering at energies around the Coulomb barrier. The folded $p+^{12,13}$C optical potentials are shown to account well for both the elastic $p+^{12,13}$C3 scattering and astrophysical $S$ factors of the radiative capture $^{12,13}$C$(p,\gamma)$ reactions.