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Global Examination of the $^{12}$C+$^{12}$C Reaction Data at Low and Intermediate Energies

We examine the $^{12}$C+$^{12}$C elastic scattering over a wide energy range from 32.0 to 70.7 MeV in the laboratory system within the framework of the Optical model and the Coupled-Channels formalism. The $^{12}$C+$^{12}$C system has been extensively studied within and over this energy range in the past. These efforts have been futile in determining the shape of the nuclear potential in the low energy region and in describing the individual angular distributions, single-angle 50$^{0}$ to 90$^{0}$ excitation functions and reaction cross-section data simultaneously. In order to address these problems systematically, we propose a potential that belongs to a family other than the one used to describe higher energy experimental data and show that it is possible to use it over this wide energy range. This potential also predicts the resonances at correct energies with reasonable widths.