Radiative α capture on 12C in cluster effective field theory: Short review

Study of radiative α capture on ¹²C, ¹²C(α,γ)¹⁶O, in cluster effective field theory (EFT) is reviewed. A low energy EFT for ¹²C(α,γ)¹⁶O at the Gamow-peak energy, $E_G=0.3$ MeV, is constructed, and the theory is first applied to the study of elastic α-¹²C scattering at low energies. The effective range parameters are fitted to the precise phase shift data of the elastic scattering and the astrophysical $S_{E1}$ factor of the E1 transition of ¹²C(α,γ)¹⁶O at $E_G$ is estimated. For the study of the E2 transition of ¹²C(α,γ)¹⁶O, we discuss a difficulty to determine the asymptotic normalization coefficient (ANC) of the subthreshold $2_1^{+}$ state of ¹⁶O from the elastic scattering data, and demonstrate the difficulty with the estimate of the astrophysical $S_{E2}$ factor of ¹²C(α,γ)¹⁶O at $E_G$. We discuss the uncertainty in the estimate of the S factors at $E_G$ in the present approach.