\begin{document}$ p + {^{14}\rm{N}}\rightarrow {^{15}\rm{O}+{\gamma}} $\end{document}, at energies of astrophysical interest, is an important process in the CNO cycle. In this project, we apply a potential model to describe both non-resonant and resonant reactions in the channels where radiative capture occurs through electric \begin{document}$ E1 $\end{document} transitions. We employed the R-matrix method to describe the ongoing reactions via \begin{document}$ M1 $\end{document} resonant transitions, when it was not possible to correctly reproduce the experimental data using the potential model. The partial components of the astrophysical S-factor are calculated for all possible electric and magnetic dipole transitions in 15O. The linear extrapolated S-factor at zero energy (S(0)) agrees well with earlier reported values for all transition types considered in this work. Based on the value of the total astrophysical S-factor, depending on the collision energy, we calculate the nuclear reaction rates for \begin{document}$ p + {^{14}\rm{N}}\rightarrow {^{15}\rm{O}+{\gamma}} $\end{document}. The computed rates agree well with the results reported in the NACRE II Collaboration and most recent existing measurements."> Radiative capture of proton through the <sup>14</sup>N(<i>p</i>,<i>γ</i>)<sup>15</sup>O reaction at low energy -
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