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We carry out realistic coupled-channels calculations for  $^{11}$Be + $^{208}$Pb reaction in order to discuss the effects of break-upof the projectile nucleus on sub-barrier fusion.  We discretize in energy the particle continuum states, which are associatedwith the break-up process, and construct the coupling form factors to thesestates on a microscopic basis.  The incoming boundary condition is employed in solving coupled-channelsequations, which enables us to define the flux for complete fusion inside theCoulomb barrier. It is shown that complete fusion cross sections aresignificantly enhanced due to the couplings to the continuum states comparedwith the no coupling case at energies below the Coulomb barrier, while they arehindered at above barrier energies.Comment: RevTex, 3 pages, 5 figure

Role of breakup processes in fusion enhancement of drip-line nuclei at energies below the Coulomb barrier