Pion-Nucleus Scattering Using Finite Binding Potentials.

A nonperturbative treatment of finite binding potentials in pion bound nucleon scattering is developed. Coupled differential equations in configuration space are derived from a model wavefunction broken into two parts. Coordinates from the source of binding to the pion and to the nucleon are used in the elastic channel, while pion nucleon center of mass coordinates are used for the excited channels. The excited channel equations are solved in closed form using a separable nonlocal pion nucleon interaction. When inserted into the elastic channel equation, a relativistically modified single particle equation for the elastically scattered meson is derived, which features an optical potential with both local and nonlocal parts. This model is used in conjunction with first order multiple scattering theory to construct pion nucleus scattering. The assumed pion nucleon interaction is taken to be s waves with threshold p wave behavior. The region around the 33 resonance is numerically studied for both the three body model and for pions on O-16.