  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.
