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We present a simultaneous analysis of the elastic scattering and fusioncross-section data of the $^{12}$C+$^{24}$Mg system around the Coulomb barrierand over energies by using the microscopic $\alpha$-$\alpha$ double foldingcluster potential within the framework of the optical model and thecoupled-channels formalism. The $\alpha$-$\alpha$ double folding clusterpotential is obtained by using the $\alpha$-cluster distribution densities ofthe nuclei in the usual double folding procedure. The microscopic potentialresults are compared with the findings of the phenomenological deep and shallowpotentials. It is subsequently shown that only phenomenological deep real,microscopic nucleon-nucleon and $\alpha$-$\alpha$ double folding clusterpotentials provide a consistent description of the angular distributions andfusion cross-section data simultaneously. The effect of the inclusion of theexcited states of the target nucleus $^{24}$Mg on the fusion cross-sectionpredictions is also determined by the coupled-channels calculations, which areshown to improve the agreement.Comment: 4 pages Latex RevTex4 with 2 EPS Figures. Accepted for publications  in Phys. Rev.

physical review. c. nuclear physics/physical review. c, nuclear physics

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α−αdouble folding cluster potential description of theC12+