The present understanding of reaction processes involving light unstable nuclei at energies around the Coulomb barrier is reviewed. The effect of coupling to direct reaction channels on elastic scattering and fusion is investigated, with the focus on halo nuclei, for which such effects are expected to be most important. With the aim of resolving possible ambiguities in the terminology a short list of definitions for the relevant processes and quantities is proposed. This is followed by a review of the experimental and theoretical tools and information presently available. The effect of breakup couplings on elastic scattering and of transfer couplings on fusion is investigated with a series of model calculations within the coupled-channels framework. The experimental data on fusion are then compared to "bare" no-coupling one-dimensional barrier penetration model calculations employing reasonably realistic double-folded potentials. On the basis of these model calculations and comparisons with experimental data, conclusions are drawn from the observation of recurring features. The total fusion cross sections for halo nuclei show a suppression with respect to the "bare" calculations at energies just above the barrier that is probably due to single neutron transfer reactions. The data for total fusion are also consistent with a possible sub-barrier enhancement; however, this observation is not conclusive and other couplings besides the singleneutron channels would be needed in order to explain any actual enhancement. We find that a characteristic feature of halo nuclei is the dominance of direct reactions over fusion at near and subbarrier energies; the main part of the cross section is related to neutron transfers, while calculations indicate only a modest contribution from the breakup process.

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The influence on fusion of coupling to the breakup process is investigated for reactions where at least one of the colliding nuclei has a sufficiently low binding energy for breakup to become an important process. Elastic scattering, excitation functions for sub-and near-barrier fusion cross sections, and breakup yields are analyzed for 6,7 Li+ 59 Co. Continuum-Discretized Coupled-Channels (CDCC) calculations describe well the data at and above the barrier. Elastic scattering with 6 Li (as compared to 7 Li) indicates the significant role of breakup for weakly bound projectiles. A study of 4,6 He induced fusion reactions with a three-body CDCC method for the 6 He halo nucleus is presented. The relative importance of breakup and bound-state structure effects on total fusion is discussed.