Application of the \(R\)-matrix method to determine the \((p,\gamma)\) cross-section

We apply the calculable \(R\)-matrix method to determine the \(p,\Gamma\) cross section. We compare our cross-section calculation for the benchmark \(^{12}\)C\((p,\gamma)^{13}\)N reaction with results from the widely used FRESCO and RADCAP codes, which use the conventional Numerov method. Our calculations are in good agreement with these codes. Furthermore, we extend the calculable \(R\)-matrix method to accommodate non-local potentials.