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

Understand

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.