We present an exact solution of a one-dimensional (1D) model: a particle of incident energy E colliding with a target which is a 1D harmonic «solid slab» with N atoms in its ground state; the Hilbert space of the target is restricted to the (N+1) states with zero or one phonon present. For the case of a short-range interaction V(z) between the particle and the surface atom supporting a bound state, an explicit nonperturbative solution of the collision problem is obtained