Uncorrelated scattering approximation for the scattering and break-up of weakly bound nuclei on heavy targets

The scattering of a weakly bound (halo) projectile nucleus by a heavy target nucleus is investigated. A new approach, called the Uncorrelated Scattering Approximation, is proposed. The main approximation involved is to neglect the correlation between the fragments of the projectile in the region where the interaction with the target is important. The formalism makes use of hyper-spherical harmonics, Raynal-Revay coefficients and momentum-localized wave functions to expand projectile channel wave functions in terms of products of the channel wave function of the individual fragments. Within this approach, the kinetic energy and angular momentum of each fragment is conserved during the scattering process. The elastic, inelastic and break-up S-matrices are obtained as an analytic combination involving the bound wave function of the projectile and the product of the S-matrices of the fragments. The approach is applied to describe the scattering of deuteron on $^{58}$Ni at several energies. The results are compared with experimental data and continuum-discretized coupled-channels calculations.