Reanalysis of $^{13}$N($p,γ$)$^{14}$O reaction and its role in stellar CNO cycle

Abstract

Within the framework of the modified potential cluster model with forbidden states, the 13 N(p, γ) 14 O reaction rate and the astrophysical S-factor are considered. It is shown that the first p 13 N resonance determines the S-factor and contributions of the M 1 and E2 transitions are negligible at energies E < 1 MeV, but are significant at high energies. The S-factor strongly depends on the 3 S1 resonance parameters. The influence of the width of the 3 S1 resonance on S-factor is demonstrated. The reaction rate is calculated and an analytical approximation for the reaction rate is proposed. A comparison of our calculation with existing data is addressed. Results of our calculations for the 13 N(p, γ) 14 O reaction rate provide the contribution to the steadily improving reaction rate database libraries. Our calculations of the 13 N(p, γ) 14 O reaction rate along with results for the rates of 14 N(p, γ) 15 O and 12 C(p, γ) 13 N processes provide the temperature range 0.13 < T9 < 0.97 for the conversion of CNO cycle to the HCNO cycle. Our results demonstrate that at early stages of a nova explosion at temperatures about 0.1 T9 and at late stages of evolution of supermassive stars at temperatures about 1.0 T9 the ignition of the HCNO cycle could occur at much lower densities of a stellar medium.