Radiative capture of proton by $^{13}\mbox{C}$ at low energy

Abstract

Radiative capture $p + {}^{13}\mathrm{C}\rightarrow {}^{14}\mathrm{N}+\gamma $ at energies bearing astrophysical consequences is one of the important processes in the CNO cycle. We focus on the possibility of describing the main contribution to the total cross section of the radiative capture process in the framework of the single-particle potential model without separation into direct and resonant transitions. In case where the single-particle potential model fails to describe other partial components, we use the R-matrix approach. The partial components of the astrophysical S-factor are calculated for all possible electric dipole transitions. The calculated value of the total S-factor at zero energy is in good agreement with earlier reported values. Based on the value of total astrophysical S-factor depending on the collision energy, we calculate the nuclear reaction rates for ${p} + {^{13}\mathrm{C}} \rightarrow {^{14}\mathrm{{N}}}+\gamma $ .