$\alpha$ scattering cross sections on ${}^{12}$C with microscopic coupled-channel calculation

Abstract

$\alpha$ elastic and inelastic scattering on ${}^{12}$C is investigated with the coupled-channel calculation using microscopic $\alpha$-${}^{12}$C potentials, which are derived by folding the Melbourne $g$-matrix $NN$ interaction with the matter and transition densities of ${}^{12}$C. These densities are obtained by a microscopic structure model of the antisymmetrized molecular dynamics combined with and without the $3\alpha$ generator coordinate method. The calculation reproduces satisfactorily well the observed elastic and inelastic cross sections at incident energies of $E_{\alpha }=130$~MeV, 172.5~MeV, 240~MeV, and 386~MeV with no adjustable parameter. Isoscalar monopole and dipole excitations to the $0_2^{+}$, $0_3^{+}$, and $1_1^{-}$ states in the $\alpha$ scattering are discussed.

Comments: 15 pages, 7 figures