Bayesian Framework for the E1 and E2 Astrophysical Factors at 300 keV from Subthreshold and Ground-State Asymptotic Normalization Coefficients
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| Format: | Preprint |
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2025
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| _version_ | 1866908654090846208 |
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| author | Mukhamedzhanov, A. M. |
| author_facet | Mukhamedzhanov, A. M. |
| contents | The $^{12}\mathrm{C}(α,γ)^{16}\mathrm{O}$ reaction governs the carbon-to-oxygen ratio set during helium burning, shaping white-dwarf structure and Type~Ia supernova yields. At the astrophysical energy $E \approx 300~\mathrm{keV}$, the cross section is controlled by the subthreshold $1^{-}$ (7.12~MeV) and $2^{+}$ (6.92~MeV) states, whose contributions depend on their asymptotic normalization coefficients (ANCs) $C_{1}$ and $C_{2}$, respectively. We perform a Bayesian analysis of the $S_{E1}(300~\mathrm{keV})$ and $S_{E2}(300~\mathrm{keV})$ factors using calibrated $R$-matrix mappings and experimental ANC constraints for the $1^{-}$, $2^{+}$, and $0^{+}$ ground state. For $S_{E1}(300~\mathrm{keV})$, flat prior on the $1^{-}$ ANC lead to broad posterior with $68\%$ credible interval spanning $ [71.4,\,93.4]$~keV\,b, while Gaussian priors concentrate weight near the reported ANC values and yield narrower posteriors. For $S_{E2}(300~\mathrm{keV})$, the analysis includes the interference of the radiative transition through the subthreshold resonance with the direct capture to the ground-state, which depends on the ground-state ANC $C_{0}$, giving broad posterior with $68\%$ credible interval spanning $[30.7,\,50.5]$~keV\,b. The Gaussian priors centered near anchor values. The resulting posteriors quantify both correlations and uncertainties: despite incorporating the published ANC constraints, the $68\%$ intervals remain broad, showing that present ANC determinations do not yet reduce the astrophysical uncertainty. Overall, the Bayesian framework provides statistically robust posteriors for $S_{E1}(300~\mathrm{keV})$ and $S_{E2}(300~\mathrm{keV})$, improving the reliability of extrapolations for stellar modeling and nucleosynthesis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_17102 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Framework for the E1 and E2 Astrophysical Factors at 300 keV from Subthreshold and Ground-State Asymptotic Normalization Coefficients Mukhamedzhanov, A. M. High Energy Astrophysical Phenomena The $^{12}\mathrm{C}(α,γ)^{16}\mathrm{O}$ reaction governs the carbon-to-oxygen ratio set during helium burning, shaping white-dwarf structure and Type~Ia supernova yields. At the astrophysical energy $E \approx 300~\mathrm{keV}$, the cross section is controlled by the subthreshold $1^{-}$ (7.12~MeV) and $2^{+}$ (6.92~MeV) states, whose contributions depend on their asymptotic normalization coefficients (ANCs) $C_{1}$ and $C_{2}$, respectively. We perform a Bayesian analysis of the $S_{E1}(300~\mathrm{keV})$ and $S_{E2}(300~\mathrm{keV})$ factors using calibrated $R$-matrix mappings and experimental ANC constraints for the $1^{-}$, $2^{+}$, and $0^{+}$ ground state. For $S_{E1}(300~\mathrm{keV})$, flat prior on the $1^{-}$ ANC lead to broad posterior with $68\%$ credible interval spanning $ [71.4,\,93.4]$~keV\,b, while Gaussian priors concentrate weight near the reported ANC values and yield narrower posteriors. For $S_{E2}(300~\mathrm{keV})$, the analysis includes the interference of the radiative transition through the subthreshold resonance with the direct capture to the ground-state, which depends on the ground-state ANC $C_{0}$, giving broad posterior with $68\%$ credible interval spanning $[30.7,\,50.5]$~keV\,b. The Gaussian priors centered near anchor values. The resulting posteriors quantify both correlations and uncertainties: despite incorporating the published ANC constraints, the $68\%$ intervals remain broad, showing that present ANC determinations do not yet reduce the astrophysical uncertainty. Overall, the Bayesian framework provides statistically robust posteriors for $S_{E1}(300~\mathrm{keV})$ and $S_{E2}(300~\mathrm{keV})$, improving the reliability of extrapolations for stellar modeling and nucleosynthesis. |
| title | Bayesian Framework for the E1 and E2 Astrophysical Factors at 300 keV from Subthreshold and Ground-State Asymptotic Normalization Coefficients |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2509.17102 |