\begin{document}$ l=2 $\end{document} and E2 transition of radiative α capture on 12C and 12C(α,γ)16O are studied in cluster effective field theory. Owing to the problem in fixing the asymptotic normalization coefficient (ANC) of the subthreshold \begin{document}$ 2_1^+ $\end{document} state of 16O or, equivalently, the effective range parameters of the \begin{document}$ 2_1^+ $\end{document} state, from the elastic scattering data, we introduced the conditions that lead to a large value of the ANC in this study. We also introduced d-wave phase shift data of the elastic scattering up to the α energy, \begin{document}$ E_\alpha=10 $\end{document} MeV, which contain the resonant \begin{document}$ 2_4^+ $\end{document} state of 16O. Applying these conditions, the parameters of the S matrix of the elastic scattering for \begin{document}$ l=2 $\end{document} were fitted to the phase shift data, and the fitted parameters were employed in the calculation of the astrophysical \begin{document}$ S_{E2} $\end{document} factor of 12C(α,γ)16O; we extrapolated the \begin{document}$ S_{E2} $\end{document} factor to the Gamow-peak energy, \begin{document}$ E_G=0.3 $\end{document} MeV. We found that the aforementioned conditions lead to significant effects in the observables of the \begin{document}$ 2_4^+ $\end{document} state of 16O and the estimate of the \begin{document}$ S_{E2} $\end{document} factor at \begin{document}$ E_G $\end{document} and confirmed that the ANC of the \begin{document}$ 2_1^+ $\end{document} of 16O cannot be determined by the phase shift data for \begin{document}$ l=2 $\end{document}."> Fixing effective range parameters in elastic <i>α</i>-<sup>12</sup>C scattering: impact on resonant 2<sub>4</sub><sup>+</sup> state of <sup>16</sup>O and <i>S</i><sub><i>E</i>2</sub> factor of <sup>12</sup>C(<i>α</i>,<i>γ</i>)<sup>16</sup>O -
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