Model for scattering from the bound state of a two-body system

An exactly solvable model for scattering of a particle from the bound state of a two-body system is studied. In this model the motion of all particles is confined to one dimension. It is also assumed that the interaction between the projectile and the target is nonlocal and separable, but the potential between the target particles is local. Depending on the form of the latter potential two cases are considered: (1) the target is the ground state of a system whose eigenvalues are discrete and eigenfunctions localized, and (2) the target has only one bound state. In both cases the problem can be solved with overlapping as well as nonoverlapping potentials. This model is used to test the accuracy of the fixed scatterer approximation. It turns out that in this approximation the two cases yield similar results