Reactive content of the Klein-Gordon optical potential

Abstract

The reactive content of the pion-nucleus optical potential is explicated in the Klein-Gordon and relativistic Schrödinger theories. It is proven that even though the solution of the Klein-Gordon equation introduces intermediate multipion states, there is no inelastic contribution of these states to the scattering amplitudes. This is shown to come about from an intricate cancellation between diagrams which contain different numbers of pions at specific intermediate times. Approximation schemes which expand the optical potential of the relativistic Schrödinger equation in terms of a fixed number of pions present at a given time are shown not to maintain this cancellation whenever truncated at any finite order of perturbation theory.