22.cm 16.cm -1.7cm -1.5cm 1.5cm 1.2em 0.5in 0.5in

[ **Elastic $\alpha$-$^{12}$C scattering at low energies with the bound states of $^{16}$O in effective field theory** ]{}

[ Shung-Ichi Ando[^1], ]{} [*School of Mechanical and ICT convergence engineering, Sunmoon University, Asan, Chungnam 31460, Republic of Korea* ]{}

The elastic $\alpha$-$^{12}$C scattering for $l=0,1,2,3$ channels at low energies is studied, including the energies of excited bound states of $^{16}$O, in effective field theory. We introduce a new renormalization method due to the large suppression factor produced by the Coulomb interaction when fitting the effective range parameters to the phase sift data. After fitting the parameters, we calculate asymptotic normalization constants of the $0_2^+$, $1_1^-$, $2_1^+$, $3_1^-$ states of $^{16}$O. We also discuss the uncertainties of the present study when the amplitudes are interpolated to the stellar energy region of the $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction.

PACS: 11.10.Ef, 24.10.-i, 25.55.Ci, 26.20.Fj

[**1. Introduction**]{}

The radiative $\alpha$ capture on carbon-12, $^{12}C(\alpha,\gamma)^{16}$O, is one of the fundamental reactions in nuclear-astrophysics, which determines the $C/O$ ratio synthesized in the stars [@f-rmp84]. The reaction rate of the process at the Gamow peak energy, $T_G=0.3$ MeV, however, cannot be determined in experiment due to the Coulomb barrier. It is necessary to 