  The Airy structure of the nuclear rainbow and prerainbow in inelastic and
elastic $\alpha+^{16}$O scattering is studied with the coupled channel method
using a folding potential derived from the microscopic wave functions of
$^{16}$O. The theoretical calculations reproduce the characteristic energy
evolution of the Airy minimum of the experimental angular distributions. The
energy levels with $\alpha$-cluster structure in $^{20}$Ne are reproduced well
using the potentials determined from the analysis of scattering. It is shown
that the emergence of the $K=0_3^+$ $\alpha$-cluster band with core excitation
at 7.19 MeV in $^{20}$Ne is intimately related to the emergence of the
prerainbow and rainbow in inelastic scattering to the $^{16}$O($0^+_2$). It is
found that the $\alpha$-cluster states with core excitation, the prerainbow and
the rainbow in inelastic scattering are understood in a unified way as well as
in the case of elastic scattering.
