The astrophysical $S-$factor and reaction rate for $^{15}$N($p,γ$)$^{16}$O within the modified potential cluster model
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913938474532864 |
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| author | Dubovichenko, S. B. Tkachenko, A. S. Kezerashvili, R. Ya. Burkova, N. A. Yeleusheva, B. M. |
| author_facet | Dubovichenko, S. B. Tkachenko, A. S. Kezerashvili, R. Ya. Burkova, N. A. Yeleusheva, B. M. |
| contents | 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($p,γ_{0}$)$^{16}$O reaction includes the consideration of $^{3}S_{1}$ resonances due to $E1$ transitions and the contribution of $^{3}P_{1}$ scattering wave in $p$ + $^{15}$N channel due to $^{3}P_{1}\longrightarrow $ $^{3}P_{0}$ $M1$ transition. We calculated the astrophysical low-energy $S-$factor, and extrapolated $S(0)$ turned out to be within $34.7-40.4$ keV$\cdot $b. The important role of the asymptotic constant (AC) for the $^{15}$N($p,γ_{0}$)$^{16}$O 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 \textit{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 $\sim $\ 1.3 at $T_{9}=1.3$.
We present the Gamow energy window and a comparison of rates for radiative proton capture reactions $^{12}$N($p,γ$)$^{13}$O, $^{13}$N($p,γ$) $^{14}$O, $^{14}$N($p,γ$)$^{15}$O, and $^{15}$N($p,γ$)$^{16}$O obtained in the framework of the MPCM and give temperature windows, prevalence, and significance of each process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14680 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The astrophysical $S-$factor and reaction rate for $^{15}$N($p,γ$)$^{16}$O within the modified potential cluster model Dubovichenko, S. B. Tkachenko, A. S. Kezerashvili, R. Ya. Burkova, N. A. Yeleusheva, B. M. Nuclear Theory Astrophysics of Galaxies Solar and Stellar Astrophysics 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($p,γ_{0}$)$^{16}$O reaction includes the consideration of $^{3}S_{1}$ resonances due to $E1$ transitions and the contribution of $^{3}P_{1}$ scattering wave in $p$ + $^{15}$N channel due to $^{3}P_{1}\longrightarrow $ $^{3}P_{0}$ $M1$ transition. We calculated the astrophysical low-energy $S-$factor, and extrapolated $S(0)$ turned out to be within $34.7-40.4$ keV$\cdot $b. The important role of the asymptotic constant (AC) for the $^{15}$N($p,γ_{0}$)$^{16}$O 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 \textit{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 $\sim $\ 1.3 at $T_{9}=1.3$. We present the Gamow energy window and a comparison of rates for radiative proton capture reactions $^{12}$N($p,γ$)$^{13}$O, $^{13}$N($p,γ$) $^{14}$O, $^{14}$N($p,γ$)$^{15}$O, and $^{15}$N($p,γ$)$^{16}$O obtained in the framework of the MPCM and give temperature windows, prevalence, and significance of each process. |
| title | The astrophysical $S-$factor and reaction rate for $^{15}$N($p,γ$)$^{16}$O within the modified potential cluster model |
| topic | Nuclear Theory Astrophysics of Galaxies Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2303.14680 |