Off-shell behavior of the crossed nucleon pole in pion-nucleus scattering

The contribution of the nucleon-pole piece of the pion-nucleon amplitude to the pion-nucleus optical potential is examined. Straightforward calculations of diagrams which are intermediate between Goldstone and Feynman diagrams produce simple results with well-behaved physical implications. In particular, the direct S-channel nucleon pole contributes to one-body true absorption while the crossed U-channel pole has a novel off-shell behavior and does not contribute to pion true absorption.