Astrophysical S Factor and Reaction Rate of ¹²C(α,γ)¹⁶O Reaction in Stellar Helium Burning

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.