The astrophysical $S-$factor and reaction rate for $^{15}$N($p,γ$)$^{16}$O within the modified potential cluster model

S. B. Dubovichenko, N. A. Burkova, R. Ya. Kezerashvili, A. S. Tkachenko, B. M. Yeleusheva

Published 2023-03-26Version 1

We study a radiative $p^{15}$N capture on the ground state of $^{16}$O at stellar energies within the framework of a modified potential cluster model (MPCM) with forbidden states, including low lying resonances. The investigation of the $^{15}$N($p,\gamma $)$^{16}$O reaction includes the consideration of $^{3}S_{1}$ resonances due to $E1$ transitions and contribution of $^{3}P_{1}$ scattering wave in $p$ + $^{15}$N channel due to $^{3}P_{1}\longrightarrow $ $^{3}P_{0}$ $M1$ transition. We calculate the astrophysical low-energy $S-$factor and extrapolated $S(0)$ turned out to be within $34.7-40.4$ keV$\cdot $b. It is elucidated the important role of the asymptotic constant (AC) for the $^{15}$N($p,\gamma $)$^{16}$O process with interfering $^{3}S_{1}$(312) and $^{3}S_{1}$(962) resonances. A comparison of our calculation for $S-$factor with existing experimental and theoretical data is addressed and the reasonable agreement is found. The reaction rate is calculated and compared with the existing rates. It has negligible dependence on the variation of AC, but shows strong impact of the interference of $^{3}S_{1}$(312) and $^{3}S_{1}$(962) resonances, especially at $T_{9}$ referring to the CNO Gamow windows. We present a stellar temperature dependence on the Gamow energy and a comparison of rates for radiative proton capture reactions for CNO cycle on nitrogen isotopes obtained in the framework of the MPCM and give temperature windows, prevalence, and significance of each process.