The effect of continuum couplings in the fusion of the halo nucleus Be-11 on Pb-208 around the Coulomb barrier is studied using a three-body model within a coupled discretized continuum channels formalism. We investigate in particular the role of continuum-continuum couplings. These are found to hinder total, complete, and incomplete fusion processes. Couplings to the projectile 1p(1/2) bound excited state redistribute the complete and incomplete fusion cross sections, but the total fusion cross section remains nearly constant. Results show that continuum-continuum couplings enhance the irreversibility of breakup and reduce the flux that penetrates the Coulomb barrier. Converged total fusion cross sections agree with the experimental ones for energies around the Coulomb barrier, but underestimate those for energies well above the Coulomb barrier.
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