Treatment of continuum in nuclear reactions involving weakly bound systems. A simple model to test different prescriptions describing the coupling to continuum states

We exploit a model describing the break-up 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 near-by 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. The comparison with the exact calculations shows that standard coupled channel descriptions based on discretization of the continuum can be accurate only when a proper choice is made of the number of discrete states, of the energy mesh and of the energy cutoff. This may imply, even in simplified cases, the use of a rather large (and unpracticable) number of channels. The use of a more restricted number of channels may lead to misleading results.