Asymptotic normalization coefficients for $α+ {}^{12}{\rm C}$ synthesis and the $S$-factor for ${}^{12}{\rm C}(α, \,γ){}^{16}{\rm O}$ radiative capture
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2023
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| author | Mukhamedzhanov, A. M. deBoer, R. J. Irgaziev, B. F. Blokhintsev, L. D. Kadyrov, A. S. Savin, D. A. |
| author_facet | Mukhamedzhanov, A. M. deBoer, R. J. Irgaziev, B. F. Blokhintsev, L. D. Kadyrov, A. S. Savin, D. A. |
| contents | The $^{12}{\rm C}(α,γ)^{16}$O reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the $^{16}$O nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, 2$^+$) and (7.12 MeV, 1$^-$), that dominate the behavior of the low-energy $S$-factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. Recently, using a model-independent extrapolation method, Blokhintsev {\it et al.} [Eur. Phys. J. A {\bf 59} (2023) 162] determined the ANCs for the $α$-particle removal taking into account three subthreshold states in $^{16}$O. The goal of this paper is to address four main problems elucidating the impact of the subthreshold ANCs on the low-energy $S$-factor. Firstly, we analyse the connection between variations of the subthreshold ANCs and the low-energy $S$-factor, in particular, at the most effective energy of $300$ keV. Secondly, we calculate contributions to the $S(300\,{\rm keV})$-factor from the subthreshold $1^{-}$ and $2^{+}$ resonances, that are controlled by the subthreshold ANCs. We also evaluate the contribution of the uncertainties of the subthreshold ANCs to the budget of the low-energy $S$-factor uncertainty, especially, the $S(300\,{\rm keV})$-factor. Thirdly, we analyse interference of the subthreshold resonances (SRs) with higher resonances and with the $E1$ and $E2$ direct captures to the ground state. Finally, we investigate a correlated effect of the subthreshold and ground-state ANCs on the low-energy $S$-factor and, in particular, on the $S(300\,{\rm keV})$-factor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_20255 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic normalization coefficients for $α+ {}^{12}{\rm C}$ synthesis and the $S$-factor for ${}^{12}{\rm C}(α, \,γ){}^{16}{\rm O}$ radiative capture Mukhamedzhanov, A. M. deBoer, R. J. Irgaziev, B. F. Blokhintsev, L. D. Kadyrov, A. S. Savin, D. A. Nuclear Theory Solar and Stellar Astrophysics The $^{12}{\rm C}(α,γ)^{16}$O reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the $^{16}$O nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, 2$^+$) and (7.12 MeV, 1$^-$), that dominate the behavior of the low-energy $S$-factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. Recently, using a model-independent extrapolation method, Blokhintsev {\it et al.} [Eur. Phys. J. A {\bf 59} (2023) 162] determined the ANCs for the $α$-particle removal taking into account three subthreshold states in $^{16}$O. The goal of this paper is to address four main problems elucidating the impact of the subthreshold ANCs on the low-energy $S$-factor. Firstly, we analyse the connection between variations of the subthreshold ANCs and the low-energy $S$-factor, in particular, at the most effective energy of $300$ keV. Secondly, we calculate contributions to the $S(300\,{\rm keV})$-factor from the subthreshold $1^{-}$ and $2^{+}$ resonances, that are controlled by the subthreshold ANCs. We also evaluate the contribution of the uncertainties of the subthreshold ANCs to the budget of the low-energy $S$-factor uncertainty, especially, the $S(300\,{\rm keV})$-factor. Thirdly, we analyse interference of the subthreshold resonances (SRs) with higher resonances and with the $E1$ and $E2$ direct captures to the ground state. Finally, we investigate a correlated effect of the subthreshold and ground-state ANCs on the low-energy $S$-factor and, in particular, on the $S(300\,{\rm keV})$-factor. |
| title | Asymptotic normalization coefficients for $α+ {}^{12}{\rm C}$ synthesis and the $S$-factor for ${}^{12}{\rm C}(α, \,γ){}^{16}{\rm O}$ radiative capture |
| topic | Nuclear Theory Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2310.20255 |