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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.

Following Weinberg, we note that for arbitrary spin the covariant spinors and the field operators can be constructed directly from Lorentz covariance. The propagator may then be defined as the vacuum expectation value of the time-ordered product of the field operators. We produce a new arbitrary-spin wave equation by inverting this propagator. The equation so produced, even at the free-particle level, is nonlocal. Explicit results for j = 1 are given and we have checked the procedure for j = 3 2 and 2 The equation does not support kinematically anomalous solutions, as do Weinberg's equations. In addition, unlike Weinberg's equations for integral spins, it has the particle and antiparticle spinors as its solutions for both fermions and bosons. No constraint equations, as required in the Rarita-Schwinger/Bargmann-Wigner formalism, are needed.

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.

An N / D dispersion theory is developed which solves crossing symmetric Low equations. The method is used to generate crossing symmetric solutions to the Chew-Low model. We show why the technique originally proposed by Chew and Low was incapable of producing solutions.

We study a time-dependent external-field model for fast particle emission in nuclear heavy-ion reactions. The relative motion of the ions is treated classically and the internal excitations are treated quantum mechanically. The model is applied to study fast nucleon emission in the reaction 16 O + 93 Nb.