Scattering Theory for the Coupled Klein-Gordon-Schrödinger Equations in Two Space Dimensions

We study the scattering theory for the coupled Klein-Gordon-Schrodinger equation with the Yukawa type interaction in two space dimensions. The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the final state