Pion-nucleus optical potential valid up to the DELTA-resonance region

Abstract

We present in this article an optical potential for the $π$-nucleus interaction that can be used in various studies involving $π$-nucleus channels. Based on earlier treatments of the low energy $π$-nucleus optical potential, we have derived a potential expression applicable from threshold up to the $Δ$-resonance region. We extracted the impulse approximation form for this potential from the $π-N$ scattering amplitude and then added to it kinematical and physical corrections. The kinematic corrections arise from transforming the impulse approximation expression from the $π-N$ center of mass frame to the $π$-nucleus center of mass frame, while the physical corrections arise mostly from the many-body nature of the $π$-nucleus interaction. By taking advantage of the experimental progress in our knowledge of the $π-N$ process, we have updated earlier treatments with parameters calculated from state-of-the-art experimental measurements.