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Coupled-Channel Effects in Collisions between Heavy Ions near the Coulomb Barrier

With the recent availability of state-of-the-art heavy-ion stable and radioactive beams, there has been a renew interest in the investigation of nuclear reactions with heavy ions. I first present the role of inelastic and transfer channel couplings in fusion reactions induced by stable heavy ions. Analysis of experimental fusion cross sections by using standard coupled-channel calculations is discussed. The role of multi-neutron transfer is investigated in the fusion process below the Coulomb barrier by analyzing $^{32}$S+$^{90,96}$Zr as benchmark reactions. The enhancement of fusion cross sections for $^{32}$S+$^{96}$Zr is well reproduced at sub-barrier energies by NTFus code calculations including the coupling of the neutron-transfer channels following the Zagrebaev semi-classical model. Similar effects for $^{40}$Ca+$^{90}$Zr and $^{40}$Ca+$^{96}$Zr fusion excitation functions are found. The breakup coupling in both the elastic scattering and in the fusion process induced by weakly bound stable projectiles is also shown to be crucial. In this lecture, full coupled-channel calculations of the fusion excitation functions are performed by using the breakup coupling for the more neutron-rich reaction and for the more weakly bound projectiles. I clearly demonstrate that Continuum-Discretized Coupled-Channel calculations are capable to reproduce the fusion enhancement from the breakup coupling in $^{6}$Li+$^{59}$Co.