Theoretical Analysis of Coupling Channels in Fusion and Elastic Scattering Reactions for 12C +208Pb, 16O+64Zn and 16O+208Pb Systems

In the present study, the reactions of fusion and elastic scattering of the stable, tightly restricted projectiles in 12C +208Pb, 16O+64Zn, and 16O+208Pb systems have been analyzed at energies close to the Coulomb barriers. The optical potential parameters were obtained by fitting both fusion and elastic scattering data. Full Coupled-Channel (CC) code, which involves the Continuum-Discretized-Coupled-Channels (CDCC) framework, has been employed to perform the calculations. The calculations are cross-sections σfusion, barrier distribution Dfusion and tunneling probability Pfusion for fusion. As well as the elastic cross section to the Rutherford cross section σelastic/σR with angle center of mass θcm, and energy center of mass Ecm and the barrier distribution of elastic scattering Delastic with energy center of mass Ecm. The results show that the fusion reaction cross section σfusion for the system 12C +208Pb do not agree with the experimental results down to the height of the Coulomb barrier Vb and the results in elastic scattering and fusion calculations are in better agreement with the experimental data. To provide a broader theoretical foundation for the optical potential, we discuss several alternative formalisms including the microscopic double folding and energy density approaches, the extended Thomas Fermi (ETF) method with Skyrme forces, and dispersive or extended optical model (EOM) frameworks that incorporate Ginocchio type phenomenology. These models help explain the observed energy dependence and demonstrate that the phenomenological Woods Saxon potential used in this work is consistent in magnitude and diffuseness with the predictions of microscopic and semi microscopic theories.