Breakup Reaction Models for Two- and Three-Cluster Projectiles

Abstract

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,

Microscopic analysis ofBe10,11elastic scattering on protons and nuclei, and breakup processes ofBe<

“…(11) and in the S-matrices [Eqs. (14)- (18)] are used for calculations of the cross sections [Eqs. (19)- (24)] in the cases of scattering and breakup of 11 Be on protons and nuclei that will be considered in the following part of our work.…”

“…[13], not only scattering but also the breakup of 11 Be in the collisions with the target nuclei 93 Nb, 181 Ta, and 238 U play a decisive role when studying the internal cluster structure of 11 Be. Indeed, the narrow peak of the momentum distributions of the breakup fragments of such a neutron-rich nucleus reflects the very large extension of its wave function, compared to that of the core nucleus 10 Be, and thus evidences the existence of the nuclear halo [14][15][16][17][18][19][20]. As was concluded in [18], namely the longitudinal component of the momentum (taken along the beam or the z-direction) provides the most accurate information on the intrinsic properties of the halo, being insensitive to details of the collision and the size of the target.…”

Microscopic analysis of11Li elastic scattering on protons and breakup processes within the9Li+2ncluster model

“…It was shown that the momentum distribution of the breakup fragments has a narrow peak, much narrower than that observed in the fragmentation of well bound nuclei. This property has been interpreted (e.g., [13][14][15][16][17][18][19]) to be related to the very large extension of the wave function, as compared to that of the core nucleus, leading to the existence of the nuclear halo. As pointed out in Ref.…”

Structure and Coulomb dissociation of 23O within the quark–meson coupling model

“…Only the full ground state wave function of the projectile, of any orbital angular momentum configuration, enters in this theory as input. Thus, unlike most of the theoretical models described in a recent review of breakup theories [32], this approach does not require the knowledge of the positions and widths of the continuum states. Hence, it is free from the uncertainties associated with the multipole strength distributions [33] that may exist in some of these theories.…”