The dynamical eikonal approximation unifies the semiclassical time-dependent and eikonal methods. It allows calculating differential cross sections for elastic scattering and breakup in a quantal way by taking into account interference effects. Good agreement is obtained with experiment for 11Be breakup on 208Pb. Dynamical effects are weak for elastic scattering.

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Calculations of the breakup of 8 B and 11 Be are performed with the aim of analyzing their sensitivity to the projectile description. Several potentials adjusted on the same experimental data are used for each projectile. The results vary significantly with the potential choice, and this sensitivity differs from one projectile to the other. In the 8 B case, the breakup cross section is approximately scaled by the asymptotic normalization coefficient of the initial bound state (ANC). For 11 Be, the overall normalization of the breakup cross section is no longer solely determined by the ANC. The partial waves describing the continuum are found to play a significant role in this variation, as the sensitivity of the phase shifts to the projectile description changes with the physical constraints imposed to the potential.

We present a description of the break-up of halo nuclei in peripheral nuclear reactions by coupling a model of the projectile motivated by Halo Effective Field Theory with a fully dynamical treatment of the reaction using the Dynamical Eikonal Approximation. Our description of the halo system reproduces its long-range properties, i.e., binding energy and asymptotic normalization coefficients of bound states and phase shifts of continuum states. As an application we consider the break-up of 11 Be in collisions on Pb and C targets. Taking the input for our Halo-EFT-inspired description of 11 Be from a recent ab initio calculation of that system yields a good description of the Coulombdominated breakup on Pb at energies up to about 2 MeV, with the result essentially independent of the short-distance part of the halo wave function. However, the nuclear dominated break-up on C is more sensitive to short-range physics. The role of spectroscopic factors and possible extensions of our approach to include additional short-range mechanisms are also discussed.

The elastic breakup of a three-body projectile on a target is studied within the eikonal approximation with full account of final-state interactions. Bound and scattering states are calculated in hyperspherical coordinates on a Lagrange mesh. A correction is introduced to avoid the divergence of breakup cross sections due to the Coulomb interaction. The eikonal approximation allows the direct calculation of various cross sections, and in particular multidifferential cross sections can be obtained. The model is applied to the breakup of 6 He on 208 Pb. The 6 He halo nucleus is described within a three-body α+n+n model involving effective αn and nn interactions. The eikonal phase is obtained from optical potentials between α and n, and the target. Around 0.8 MeV, the total breakup cross sections exhibit a narrow 2 + resonant peak superimposed over a broad bump corresponding to a 1 − resonance. These results suffer from a disagreement with experimental data at 240 MeV/nucleon, where cross sections are much smaller at low energies. The obtained E1 strength distribution resembles other theoretical results and reopens a long-standing problem about the existence of a 1 − low-energy resonance in the 6 He continuum.

Breakup reactions are one of the main tools for the study of exotic nuclei, and in particular of their continuum. In order to get valuable information from measurements, a precise reaction model coupled to a fair description of the projectile is needed. We assume that the projectile initially possesses a cluster structure, which is revealed by the dissociation process. This structure is described by a few-body Hamiltonian involving effective forces between the clusters. Within this assumption, we review various reaction models. In semiclassical models, the projectile-target relative motion is described by a classical trajectory and the reaction properties are deduced by solving a time-dependent Schrödinger equation. We then describe the principle and variants of the eikonal approximation: the dynamical eikonal approximation, the standard eikonal approximation, and a corrected version avoiding Coulomb divergence. Finally, we present the continuum-discretized coupled-channel method (CDCC), in which the Schrödinger equation is solved with the projectile continuum approximated by square-integrable states. These models are first illustrated by applications to two-cluster projectiles for studies of nuclei far from stability and of reactions useful in astrophysics. Recent extensions to threecluster projectiles, like two-neutron halo nuclei, are then presented and discussed. We end this review with some views of the future in breakup-reaction theory. D. Baye Physique Quantique, C.P. 165/82 and Physique Nucléaire Théorique et Physique Mathématique, C.P. 229, Université Libre de Bruxelles,