Heavy-ion reactions with weakly-bound systems: a simple model

We propose a simple model describing the break-up of weakly-bound nuclei that can be used as a laboratory for testing different prescriptions that have been advanced to take into account the presence of continuum states. The model describes the evolution of a single particle wave function in one dimension, initially bound by a Woods-Saxon type potential and then perturbed by a time- and position-dependent external field. Proper choices of this potential can simulate the effect of the interaction between reaction partners in a nuclear collision. These processes generate inelastic excitation probabilities that distributed over the bound and continuum states of the system - lead to either a partial or a total fragmentation of the final wave function.