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

$\alpha$ 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.