| In the ?rst stage of stellar helium burning(stellar core temperature T ～0.2×108K) the triple-α reaction is the dominating process, while later after the build up of a signi?cant carbon abundance the12C(α,γ)16O reaction is controlling this burning phase. The reaction rate of12C(α,γ)16O and triple-α reactions compete to determine the relative abundances of oxygen and carbon prior to core-C burning. At T9=0.2, the rate of12C(α,γ)16O is the beginning condition of the following nucleosynthesis and star evolution of massive stars. The work of many investigators has resulted in a knowledge of the predicted reaction rate of 3α process to about 12% precision, accuracy at the usual helium-burning temperatures,but the published rate values of12C(α,γ)16O contradict each other strongly and their uncertainties are 2 times larger than the required precision(～10%). W. A.Fowler, a Nobel laureate in physics in 1983, de?nitely held the view that the abundance ratio of12 C to16O and the solar neutrino problem are serious di?culties in the most basic concepts of nuclear astrophysics, and designated the investigating of the origin of12 C and16O, as the ”holy grail” of nuclear astrophysics.At Ec.m.= 0.3 MeV, the cross section is about 10-17 barn. Obviously, it is too small to be measured. The most direct and trustworthy way to obtain the reaction rate of the12C(α, γ)16O reaction is to measure the cross section for that reaction to as low energy as possible, and to extrapolate to energies of astrophysical interest. To investigate the speci?c role of the16 O nucleus for the S factor,a wealth of experimental data have been accumulated over the past few decades,including the precise measurements of total cross-section of12C(α, γ)16O, γ-ray angular distributions of ground state transition, cascade transitions, β-delayedα spectra for16 N, transfer reaction of12C(6Li,d)16O and12C(7Li,t)16O, elastic scattering12C(α, α)12C and additional particle reaction pathways12C(α, α1)12C and12C(α, p)15N at high energies. But the lowest C.M. for12C(α,γ)16O cross section measurement is 891 keV, with a uncertainty lager than 50%. Despite ?ve decades of theoretical investigations yet, the desired accuracy and precision as-sociated with the extrapolated S factor of12C(α, γ)16O reaction continues to be an obstacle. R-matrix analysis is the most e?ective method for the ?tting and extrapolation of existing data of16 O system, which are main content of this work.Firstly, based on the classical R-matrix theory of Lane and Thomas, we have developed Reduced R-matrix Theory, which treats ?ve primary transitionsγn+16On(n=0,1,2,3,4) as the independent reaction channels in the channel spin representation. With the coordination of covariance statistics and error propagation theory, a global ?tting for almost all available experimental data of16 O system have been multi-iteratively analyzed by our powerful code. A reliable,accurate and self-consistent astrophysical S factor of12C(α, γ)16O has been obtained with a recommended value Stot(300) = 162.7 ± 7.3 keV b, for the ?rst time, meet the required precision.The astrophysical reaction rates at stellar temperatures 0.04 T9 10,calculated from the self-consistent S factor by our R-matrix method, is provided in both tabular form and an analytic expression. And the contributions of the reaction rate corresponding to the di?erent reaction channels, γn+16On(n=0, 1,2, 3, 4), are given. Some comparisons and discussion about our new12C(α, γ)16O reaction rate to the previous published rates are presented. The12C(α, γ)16O reaction rate at T9= 0.2 is(7.83 ± 0.35)×1015cm3mol-1s-1. These results could help scientists understand the nucleo synthesis of the intermediate-mass elements to iron element, the reaction mechanism of s-process, r-process, and p-process, and the evolution of a massive stars. Finally, a new constraint of the supernovae production factor of some isotopes are illustrated according to our12C(α, γ)16O reaction rates. |
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