We carry out realistic coupled-channels calculations for 11 Be + 208 Pb reaction in order to discuss the effects of break-up of the projectile nucleus on sub-barrier fusion. We discretize in energy the particle continuum states, which are associated with the break-up process, and construct the coupling form factors to these states on a microscopic basis. The incoming boundary condition is employed in solving coupled-channels equations, which enables us to define the flux for complete fusion inside the Coulomb barrier. It is shown that complete fusion cross sections are significantly enhanced due to the couplings to the continuum states compared with the no coupling case at energies below the Coulomb barrier, while they are hindered at above barrier energies.Quantum tunneling in systems with many degrees of freedom [1] has attracted much interest in recent years in many fields of physics and chemistry [2]. In nuclear physics, heavy-ion fusion reactions at energies near and below the Coulomb barrier are typical examples for this phenomenon. In order for fusion processes to take place, the Coulomb barrier created by the cancellation between the repulsive Coulomb force and the attractive nuclear interaction has to be overcome. It has by now been well established that the coupling of the relative motion of the colliding nuclei to nuclear intrinsic excitations as well as to transfer reaction channels cause large enhancements of the fusion cross section at subbarrier energies over the predictions of a simple barrier penetration model [3].The effect of break-up processes on fusion, on the other hand, has not yet been understood very well, and many questions have been raised during the last few years both from the experimental [4][5][6][7][8] and theoretical [9-12] points of view. The issue has become especially relevant in recent years due to the increasing availability of radioactive beams. These often involve weakly-bound systems close to the drip lines for which the possibility of projectile dissociation prior to or at the point of contact cannot be ignored. Different theoretical approaches to the problem have led to controversial results, not only quantitatively but also qualitatively. The probability for fusion at energies below the barrier has been in fact predicted to be either reduced [9,10] or enhanced [11,12] by the coupling to the continuum states.These investigations, however, were not satisfactory in view of the rather simplified assumptions used in the treatment of both the structure and reaction aspects of the problem.

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