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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.03600 |
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Table of Contents:
- The triple-$α$ reaction from the ternary continuum states at off-resonant energies, $α+α+α\rightarrow^{12}$C, remains an open question. This direct process is scrutinized using a non-adiabatic Faddeev hyperspherical harmonics $R$-matrix expansion method, and the derived reaction rates are discussed. After reviewing the model, the resultant photo-disintegration of $^{12}$C($2^+_1\rightarrow 0^+$) is shown to be much smaller than the values predicted by the adiabatic models for $0.15 \le E \le 0.35$ MeV. Despite the large difference, the derived reaction rates are illustrated to be concordant with the current evaluated rates for $0.08 \le T_9 \le 3$. The difference below $E=0.20$ MeV can be seen in the rates for $T_9 \le 0.07$. In comparison with the calculations, the rates are found to be reduced by a factor of 10$^{-4}$ at $T_9=0.05$, because of an accurate description for $^8$Be break-up. Uncertainties of the rates are also estimated by examining the sensitivity to the 3$α$ potentials. By introducing three-body $S$-factors and a resonant term, the present rates are expressed in an analytic form, and they are provided in a tabular form for astrophysical applications. To update the evaluated rates, non-resonant sequential process between $α+^8$Be could be removed. The astrophysical impact is not expected to be large, although the rates are reduced around $T_9=0.05$.