The 12C(p, γ )13N reaction is the first process in the CNO cycle. Also it is a source of low-energy solar neutrinos in various neutrino experiments. Therefore, it is of high interest to gain data of the astrophysical S-factor in low energies. By applying Faddeev’s method, we calculated wave functions for the bound state of 13N. Then the cross sections for resonance and non-resonance were calculated through using Breit–Wigner and direct capture cross section formulae, respectively. After that, we calculated the total S-factor and compared it with previous experimental data, revealing a good agreement altogether. Then, we extrapolated the S-factor in zero energy and the result was 1.32 ± 0.19 (keV.b). In the end, we calculated reaction rate and compared it with NACRE data.
