Fixing effective range parameters in elasticα-¹²C scattering: impact on resonant 2₄⁺state of¹⁶O andS_E2factor of¹²C(α,γ)¹⁶O

Abstract：

Elastic α- ¹²C scattering for $ l=2 $ and E2 transition of radiative αcapture on ¹²C and ¹²C( α, γ) ¹⁶O are studied in cluster effective field theory. Owing to the problem in fixing the asymptotic normalization coefficient (ANC) of the subthreshold $ 2_1^+ $ state of ¹⁶O or, equivalently, the effective range parameters of the $ 2_1^+ $ state, from the elastic scattering data, we introduced the conditions that lead to a large value of the ANC in this study. We also introduced d-wave phase shift data of the elastic scattering up to the αenergy, $ E_\alpha=10 $ MeV, which contain the resonant $ 2_4^+ $ state of ¹⁶O. Applying these conditions, the parameters of the Smatrix of the elastic scattering for $ l=2 $ were fitted to the phase shift data, and the fitted parameters were employed in the calculation of the astrophysical $ S_{E2} $ factor of ¹²C( α, γ) ¹⁶O; we extrapolated the $ S_{E2} $ factor to the Gamow-peak energy, $ E_G=0.3 $ MeV. We found that the aforementioned conditions lead to significant effects in the observables of the $ 2_4^+ $ state of ¹⁶O and the estimate of the $ S_{E2} $ factor at $ E_G $ and confirmed that the ANC of the $ 2_1^+ $ of ¹⁶O cannot be determined by the phase shift data for $ l=2 $ .