Field theoretic aspects of meson-nucleus scattering

Abstract

Field theoretic aspects of the pion field interacting with a nucleus are investigated. The quantum field nature of the pion is shown to be most simply and fundamentally incorporated into multiple scattering theory through the Klein-Gordon equation. This is accomplished so that crossing symmetry of the scattering amplitude is manifest and can be maintained without recourse to nonlinear equations. We give specific examples of calculating the first and second order optical potential in the static approximation. Our approach provides a clean separation between the energy and momentum dependence of the pion-nucleon amplitude and does not have the strong momentum cutoffs or the spurious reactive content of other approaches. An off-shell extrapolation of the pion-nucleon amplitude in terms of the four-momenta is required for the evaluation of second and higher order contributions to the optical potential. We discuss the conditions under which our static field theory can be regarded as a limit of a theory which allows for nucleon recoil.