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Determination of the stellar reaction rate for 12C($\alpha$, $\gamma$)16O: using a new expression with the reaction mechanism
Xu Yi(徐毅), Xu Wang(徐望) Ma Yu-Gang(马余刚), Cai Xiang-Zhou(蔡翔舟), Chen Jin-Gen(陈金根), Fan Gong-Tao(范功涛), Fan Guang-Wei(樊广伟), Guo Wei(郭威), Luo Wen(罗文), Pan Qiang-Yan(潘强岩), Shen Wen-Qing(沈文庆), and Yang Li-Feng(杨利峰)
Chin. Phys. B, 2009, 18 (4):
1421-1427.
DOI: 10.1088/1674-1056/18/4/023
The astrophysical reaction rate of $^{12}$C($\alpha$, $\gamma$)$^{16}$O plays a key role in massive star evolution. However, this reaction rate and its uncertainties have not been well determined yet, especially at $T_{9}$=0.2. The existing results even disagree with each other to a certain extent. In this paper, the E1, E2 and total (E1+E2) $^{12}$C($\alpha$, $\gamma$)$^{16}$O reaction rates are calculated in the temperature range from $T_{9}$=0.3 to 2 according to all the available cross section data. A new analytic expression of the $^{12}$C($\alpha$, $\gamma$)$^{16}$O reaction rate is brought forward based on the reaction mechanism. In this expression, each part embodies the underlying physics of the reaction. Unlike previous works, some physical parameters are chosen from experimental results directly, instead of all the parameters obtained from fitting. These parameters in the new expression, with their 3$\sigma$ fit errors, are obtained from fit to our calculated reaction rate from $T_{9}$=0.3 to 2. Using the fit results, the analytic expression of $^{12}$C($\alpha$, $\gamma$)$^{16}$O reaction rate is extrapolated down to $T_{9}$=0.05 based on the underlying physics. The $^{12}$C($\alpha$, $\gamma$)$^{16}$O reaction rate at $T_{9}$=0.2 is $(8.78\pm1.52)\times10^{15}$\,cm$^{3}$s$^{-1}$mol$^{-1}$. Some comparisons and discussions about our new $^{12}$C($\alpha$, $\gamma$)$^{16}$O reaction rate are presented, and the contributions of the reaction rate correspond to the different part of reaction mechanism are given. The agreements of the reaction rate below $T_{9}$=2 between our results and previous works indicate that our results are reliable, and they could be included in the astrophysical reaction rate network. Furthermore, we believe our method to investigate the $^{12}$C($\alpha$, $\gamma$)$^{16}$O reaction rate is reasonable, and this method can also be employed to study the reaction rate of other astrophysical reactions. Finally, a new constraint of the supernovae production factor of some isotopes are illustrated according to our $^{12}$C($\alpha$, $\gamma$)$^{16}$O reaction rates.
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