摘要: 恒星氦燃烧阶段3α反应和¹²C（α，γ）¹⁶O反应相互竞争，两者的反应率共同决定了氦燃烧结束后¹²C与¹⁶O的丰度比，该比值是大质量恒星后继演化以及伴随的元素核合成过程的初始条件。目前，氦燃烧¹²C（α，γ）¹⁶O反应起始T₉=0.2处，天体物理模型要求的反应率的精确度要低于10%，然而尚未有实验或理论给出满足要求的结果。最为直接和可靠地获取¹²C（α，γ）¹⁶O反应率的方法，就是尽可能往低能区测量其天体物理S因子，然后通过理论外推到感兴趣的能区。为此基于经典的R-矩阵理论，建立了适用于低能核反应的多道、多能级的约化R-矩阵理论来拟合几乎所有可用的¹⁶O系统的实验数据。配合使用协方差统计和误差传播理论，拟合外推得到了客观的、内部自恰的和唯一性好的¹²C（α，γ）¹⁶O反应天体物理S因子。总的外推S因子STOT（0.3 MeV）=162.7±7.3 keV·b，理论上首次给出达到恒星演化与元素核合成模型的最低要求的S因子。基于计算给出的全能区的S因子，数值积分给出了温度位于0.04 6 T₉ 6 10的¹²C（α，γ）¹⁶O天体物理反应率。在T₉=0.2处，推荐的反应率为（7.83 ±0.35）×10^-15 cm³mol^-1s^-1。


During stellar helium burning, the rates of 3α and the ¹²C(α,γ)¹⁶O reaction, in competition with one another, determine the relative abundances of ¹²C and ¹⁶O in a massive star. The abundance ratio is the beginning condition of the following nucleosynthesis and star evolution of massive stars, which are extremely sensitive to the rate of ¹²C(α,γ)¹⁶O reaction at T₉=0.2. The most direct and trustworthy way to obtain the reaction rate of the ¹²C(α,γ)¹⁶O reaction is to measure the S factor for that reaction to as low energy as possible, and to extrapolate to energies of astrophysical interest. Based on a new multilevel and multichannel reduced R-matrix theory for applications in nuclear astrophysics, we have obtained an accurate and self-consistent astrophysical S factor of ¹²C(α,γ)¹⁶O, by a global fitting for almost all available experimental data of ¹⁶O system, with the coordination of covariance statistics and error-propagation theory. The extrapolated S factor of ¹²C(α,γ)¹⁶O was obtained with a recommended value STOT (0.3 MeV)=162.7±7.3 keV·b. And the reaction rates of ¹²C(α,γ)¹⁶O for stellar temperatures between 0.04 6 T₉ 6 10 are provided. At T₉=0.2, the reaction rate is (7.83 ±0.35)×10^-15 cm³mol^-1s^-1, where stellar helium burning occurs.