Abstract
A derivation of the elastic scattering differential cross section, within a three-body eikonal model, that treats both central and spin-orbit interactions between the constituent projectile clusters and the target is presented. This formalism is then used in the theoretical study of the scattering of 8B from 12C at 40 MeV/nucleon. The proton halo candidate, 8B, is taken to consist of a single valence proton orbiting a 7Be core cluster. Calculation of the elastic scattering amplitude relies upon determining the phase shifts caused as the projectile passes through the region of interaction with the target. A form for the orbital angular momentum operator of each projectile cluster about the target is obtained that allows a relatively simple form for the spin-orbit phase shift functions, analogous to those for the central interactions, to be deduced. The study of the angular distribution of the elastic scattering differential cross section is carried out in two parts. Initially the effect of elastic break-up and recombination of the projectile during the scattering process, only taking into account central interactions, is studied. To gauge the magnitude of these effects, within the three-body model, the elastic scattering differential cross section, in the limit of no projectile break-up, is derived. Despite the very small binding energy of 8B it is shown that these effects are quite small. It is also shown, however, that these effects become more conspicuous as the valence proton becomes less localised about the core. Finally the effect of including spin-orbit interactions is studied. In the system under study these effects are shown to have an almost negligible effect on the angular distribution of the differential cross section. However, increasing the projectile kinetic energy to the region of hundreds of MeV/nucleon is seen to increase their significance. Future calculations hope to look at the angular distribution of the elastic scattering differential cross section and vector and tensor analysing powers of polarised beams of deuterons as these systems are expected to show more sensitivity to spin- orbit interactions. Furthermore, with the possibility of polarised beams of halo nuclei, the three-body Glauber model would be an ideal theoretical tool with which to study certain of their spin-related phenomena too.