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

Abstract

We study a radiative p 15N 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,γ0)16O reaction includes the consideration of 3 S 1 resonances due to E1 transitions and the contribution of 3 P 1 scattering wave in p + 15N channel due to 3 P 1 → 3 P 0 M1 transition. We calculated the astrophysical low-energy S-factor, and 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,γ0)16O process with interfering 3 S 1(312) and 3 S 1(962) resonances is elucidated. A comparison of our calculation for 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, especially at temperatures, referring to the CNO Gamow windows. We estimate the contribution of cascade transitions to the reaction rate based on the exclusive experimental data by Imbriani, et al. 2012. The reaction rate enhancement due to the cascade transitions is observed from T 9 > 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,γ)13O, 13N(p,γ)14O, 14N(p,γ)15O, and 15N(p,γ)16O obtained in the framework of the MPCM and give temperature windows, prevalence, and significance of each process.