The scattering cross-section is calculated tor the problem of a particle incident on another bound to the origin. The scattered par ticle interacts both with the fixed potential at the origin and the bound particle. Two solutions are obtained: one for the case where the two particles are similar and one for the case where they are dis similar. The motion of each particle is one-dimensional, and the inter actions are artificially chosen so that the Schrodinger equation is integrable. Thus, although the model chosen here has no physical reali ty. It is expected that the results will be useful in evaluating ap proximation techniques for physical particle scattering problems.