Research progress on astrophysical S factor and reaction rate for ¹²C(α,γ)¹⁶O in stellar helium burning

Based on a new multilevel and multichannel reduced R-matrix theory for applications in nuclear astrophysics, researchers from Shanghai Institute of Applied Physics, CAS and Tsinghua University have obtained an accurateand self-consistent astrophysical S factor and reaction rate of ¹²C(α,γ)¹⁶O, by a global fitting for almost all available experimental data of ¹⁶O system. The series work were published in Astrophysical Journal Letters (ApJ, 817, L5 (2016)) and Physical Review C (PRC 92,045802 (2015)), for the first time, which could meet the required precision of stellar models in theoretical extrapolation.  

During stellar helium burning, the rates of 3α and the ¹²C(α,γ)¹⁶O reaction, in competition with one another, determine the timescale of this phase and the relative abundances of ¹²C and ¹⁶O in a massive star. The abundance ratio is the beginning condition of the following nucleo synthesis and star evolution of massive stars, which are extremely sensitive to the rate of ¹²C(α,γ)¹⁶O reaction at T₉ = 0.2. William A. Fowler, a Nobel laureate in physics in 1983, definitely held a view that the abundance ratio of ¹²C to ¹⁶O and the solar neutrino problem are the most basic questions of nuclear astrophysics. The most direct and trustworthy way to obtain the astrophysical 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. 

Recently, Mr. Zhendong An, Prof. Yu-Gang Ma and his team at SINAP, together with Prof. Zhenpeng Chen from Tsinghua University, have developed a multilevel and multichannel reduced R-matrix theory based on the classical R-matrix theory of Lane and Thomas, for low-energy nuclear reaction. With the coordination of covariance statistics and error-propagation theory, a global fitting for almost all available experimental data of ¹⁶O system has been multi-iteratively analyzed by the powerful code. The extrapolated S factor of ¹²C(α,γ)¹⁶O was obtained with a recommended value Stot (0.3MeV) = 162.7±7.3 keV b. And the reaction rates of ¹²C(α,γ)¹⁶O for stellar temperatures between 0.04 ≤T₉≤ 10 are provided in a tabular form and by an analytical fitting expression. At T₉ = 0.2, the reaction rate is (7.83 ± 0.35) × 10¹⁵ cm³ mol^？1 s^？1, where stellar helium burning occurs. 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. 

The undergoing project of Shanghai Laser Electron Gamma Source facility (SLEGS) at SSRF-II plans to allow a measurement of cross sections in the pb region, and hopes to resolve the "holy grail" problem of ¹²C(α,γ)¹⁶O reaction experimentally. 

This work is partially supported by the National Natural Science Foundation of China and the 973 project. 

Contact  

Yugang Ma 

Shanghai Institute of Applied Physics (SINAP), CAS 

Email: mayugang@sinap.ac.cn 

FIG 1. The Best fits to the Stot data.


FIG 2、Comparisons of the astrophysical reaction rate of ¹²C(α, γ)¹⁶O normalized to our new recommended rate.