  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.
