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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.

Elastic differential cross sections for K + mesons scattered from nat C and 6 Li targets have been measured at an incident momentum of 715 MeV/c and at angles of 7° to 42° in the laboratory frame. The experimental cross sections agree, within errors, with two different parameter-free impulse approximation calculations. To reduce the effects of the systematic errors, the ratio of the experimental cross sections for nat C to 6 Li is compared to the theoretical values, and these ratios do not agree with theory. This discrepancy suggests either a density-dependent alteration of K + -nucleon amplitudes or a failure of the optical potential calculations to describe these nuclides adequately.

A model for the resonant pion-nucleon D- and F-waves is developed which assumes that the pion-plus-nucleon couples to a resonance and that the resonance can serve as a doorway to the inelastic channels. With the use of simple form factors, the model is capable of reproducing the pion-nucleon phase shifts up to an energy of T π = 1.4 GeV if the coupling of the elastic channel to the inelastic channels is taken from data as input into the model. A value for the mass of the resonance that would result in the absence of the coupling to decay channels is extracted from the data utilizing the model. This is the mass that is most easily modeled by bag models. For the non-resonant D- and F-wave channels a separable potential model is used. This model, like the resonance model, is developed utilizing the invariant amplitude which is free of kinematic singularities and uses invariant norms and phase spaces. The model is also applied to the S-wave channels. A relation between the resonance model and the Chew-Low model is discovered and used to derive an extended Chew-Low model which is applied to the P 13 , P 31 , and P 33 channels. Implications of the model for understanding the range of the pion-nucleon interaction and the dynamic structure of the interaction are presented.