Astrophysical S factor of {¹²C(α,γ)¹⁶O} Calculated with the Reduced R-matrix Theory

Determination of the accurate astrophysical S factor of {$^{12}$C($\alpha,\gamma$)$^{16}$O} reaction has been regarded as a holy grail of nuclear astrophysics for decades. In current stellar models, a knowledge of that value to better than 10\% is desirable. Due to the practical issues, tremendous experimental and theoretical efforts over nearly 50 years are not able to reach this goal, and the published values contradicted with each other strongly and their uncertainties are 2 times larger than the required precision. To this end we have developed a Reduced R-matrix Theory, based on the classical R-matrix theory of Lane and Thomas, which treats primary transitions to ground state and four bound states as the independent reaction channels in the channel spin representation. With the coordination of covariance statistics and error propagation theory, a global fitting for almost all available experimental data of $^{16}$O system has been multi-iteratively analyzed by our powerful code. A reliable, accurate and self-consistent astrophysical S factor of {$^{12}$C($\alpha,\gamma$)$^{16}$O} was obtained with a recommended value $S_{tot}$ (300) = 162.7 $\pm$ 7.3 keV b (4.5\%) which could meet the required precision.