Astrophysical S-factor and reaction rate for 15N(p,γ)16O within the modified potential cluster model

We study radiative $ p^{15} {\rm{N}}$ capture on the ground state of ¹⁶O at stellar energies within the framework of a modified potential cluster model (MPCM) with forbidden states, including low-lying resonances. The investigation of the ¹⁵N( $ p, \gamma _{0} $ )¹⁶O reaction includes the consideration of $ {}^{3}S_{1} $ resonances due to $ E1 $ transitions and the contribution of the $ {}^{3}P_{1} $ scattering wave in the p + ¹⁵N channel due to the $ {}^{3}P_{1}\longrightarrow $ $ {}^{3}P_{0} $ $ M1 $ transition. We calculated the astrophysical low-energy S-factor, and the extrapolated $ S(0) $ turned out to be within 34.7-40.4 keV·b. The important role of the asymptotic constant (AC) for the ¹⁵N( $ p, \gamma _{0} $ )¹⁶O process with interfering $ {}^{3}S_{1} $ (312) and $ {}^{3}S_{1} $ (962) resonances is elucidated. A comparison of our calculation for the S-factor with existing experimental and theoretical data is addressed, and a 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 a strong impact of the interference of $ {}^{3}S_{1} $ (312) and $ {}^{3}S_{1} $ (962) resonances in reference to the CNO Gamow windows, especially at low temperatures. We estimate the contribution of cascade transitions to the reaction rate based on the exclusive experimental data from Phys. Rev. C. 85, 065810 (2012). The reaction rate enhancement due to the cascade transitions is observed from $ T_{9} \gt 0.3 $ and reaches the maximum factor ~ 1.3 at $ T_{9}=1.3 $ . We present the Gamow energy window and a comparison of rates for radiative proton capture reactions ¹²N( $ p, \gamma $ )¹³O, ¹³N( $ p, \gamma $ ) ¹⁴O, ¹⁴N( $ p, \gamma $ )¹⁵O, and ¹⁵N( $ p, \gamma $ )¹⁶O obtained in the framework of the MPCM and provide the temperature windows, prevalence, and significance of each process. *Supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan (AP09259174)