Role of the continuum in reactions with weakly bound systems: A comparative study between the time evolution of a break-up wave function and its coupled-channel approximation

We exploit a model describing the breakup of weakly bound nuclei that can be used as a laboratory for testing different prescriptions that have been advanced in the literature to take into account the nearby presence of continuum states. In the model, we follow 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.