Calculation of astrophysical S-factor in reaction $^{13}\mathrm{C}(p,\gamma )^{14}\mathrm{N}$ for first resonance levels

The \(^{13}\mathrm{C}(p,\gamma )^{14}\mathrm{N}\) reaction is one of the important reactions in the CNO cycle, which is a key process in nucleosynthesis. We first calculated wave functions for the bound state of \(^{14}\mathrm{N}\) with Faddeev’s method. In this method, the considered reaction components are \(^{12}\mathrm{C}+n+p\). Then, by using direct capture cross section and Breit–Wigner formulae, the non-resonant and resonant cross sections were calculated, respectively. In the next step, we calculated the total S-factor and compared it with experimental data, which showed good agreement between them. Next, we extrapolated the S-factor for the transition to the ground state at zero energy and obtained \(S(0)=5.8 \pm 0.7~(\mbox{keV}\,\mbox{b})\) and then calculate reaction rate. These ones are in agreement with previous reported results.