  We present a simultaneous analysis of the elastic scattering and fusion
cross-section data of the $^{12}$C+$^{24}$Mg system around the Coulomb barrier
and over energies by using the microscopic $\alpha$-$\alpha$ double folding
cluster potential within the framework of the optical model and the
coupled-channels formalism. The $\alpha$-$\alpha$ double folding cluster
potential is obtained by using the $\alpha$-cluster distribution densities of
the nuclei in the usual double folding procedure. The microscopic potential
results are compared with the findings of the phenomenological deep and shallow
potentials. It is subsequently shown that only phenomenological deep real,
microscopic nucleon-nucleon and $\alpha$-$\alpha$ double folding cluster
potentials provide a consistent description of the angular distributions and
fusion cross-section data simultaneously. The effect of the inclusion of the
excited states of the target nucleus $^{24}$Mg on the fusion cross-section
predictions is also determined by the coupled-channels calculations, which are
shown to improve the agreement.
