S matrices of elastic α−C12 scattering at low energies in effective field theory

Abstract

The elastic $\ensuremath{\alpha}\text{\ensuremath{-}}^{12}\mathrm{C}$ scattering at low energies for $l=0,1,2,3,4,5,6$ is studied in effective field theory. I discuss the construction of the $S$ matrices of elastic $\ensuremath{\alpha}\text{\ensuremath{-}}^{12}\mathrm{C}$ scattering in terms of the amplitudes of subthreshold bound and resonant states of $^{16}\mathrm{O}$, which are calculated from the effective Lagrangian. The parameters appearing in the $S$ matrices are fitted to the phase shift data below the $p\text{\ensuremath{-}}^{15}\mathrm{N}$ breakup threshold energy, and one finds that the phase shifts are well described within the theory.