Fixing effective range parameters in elastic <i>α</i>-¹²C scattering: impact on resonant 2₄ ⁺ state of ¹⁶O and <i>S</i> _<i>E</i>2 factor of ¹²C(<i>α</i>,<i>γ</i>)¹⁶O*

Abstract Elastic α - 12 C scattering for and E 2 transition of radiative α capture on 12 C and 12 C( α , γ ) 16 O are studied in cluster effective field theory. Owing to the problem in fixing the asymptotic normalization coefficient (ANC) of the subthreshold state of 16 O or, equivalently, the effective range parameters of the 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 α energy, MeV, which contain the resonant state of 16 O. Applying these conditions, the parameters of the S matrix of the elastic scattering for were fitted to the phase shift data, and the fitted parameters were employed in the calculation of the astrophysical factor of 12 C( α , γ ) 16 O; we extrapolated the factor to the Gamow-peak energy, MeV. We found that the aforementioned conditions lead to significant effects in the observables of the state of 16 O and the estimate of the factor at and confirmed that the ANC of the of 16 O cannot be determined by the phase shift data for .