Astrophysical aspects of ${}^{12}$C$(p,\gamma {)}^{13}$N reaction

The Carbon-Nitrogen-Oxygen (CNO) cycle is fundamental to the process of hydrogen burning in stars, serving as a pivotal mechanism. At its core, the primary reaction involves the radiative capture of a proton by ${}^{12}$C, crucially influencing the isotopic ratio of ${}^{12}$C to ${}^{13}$C observed in celestial bodies, including our Solar System. We have addressed this reaction mechanism by extrapolating to low-energy cross sections and S-factors with the aid of astrophysical R-matrix. Our investigation aims to shed light on its implications for nuclear reaction rates, thus influencing the abundance ratio of ${}^{12}$C to ${}^{13}$C in the cosmic environment.