Reanalysis of ${}^{13}$N($p,\gamma$)${}^{14}$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($p,\gamma$)${}^{14}$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 $M1$ and $E2$ transitions are negligible at energies $E<1$ MeV, but are significant at high energies. The $S$-factor strongly depends on the ${}^3{S}_1$ resonance parameters. The influence of the width of \ the ${}^3{S}_1$ 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($p,\gamma {)}^{14}$O reaction rate provide the contribution to the steadily improving reaction rate database libraries. Our calculations of the N($p,\gamma {)}^{14}$O reaction rate along with results for the rates of ${}^{14}$N(O and ${}^{12}$C$(p,\gamma {)}^{13}$N processes provide the temperature range $0.13<T_9<0.97$ for the conversion of CNO cycle to the HCNO cycle. Our results demonstrate that at early stages of a nova explosion at temperatures about $0.1$ $T_9$ and at late stages of evolution of supermassive stars at temperatures about $1.0$ $T_9$ the ignition of the HCNO cycle could occur at much lower densities of a stellar medium.

Comments: 19 pages, 8 figures