Relativistic wave functions for pion-nucleon and pion-nucleus scattering

Abstract

We use a modification of the method of Blankenbecler and Sugar to discuss various reductions of the Bethe-Salpeter equation to three-dimensional equations. Pion-nucleon and pion-nucleus scattering are treated, and the advantages of the use of different Green's functions are indicated. For the case of pion-nucleus scattering we propose a relativistic impulse approximation for use in construction of a relativistic optical model. The relations of the wave functions resulting from the solution of the three-dimensional equations to the Bethe-Salpeter wave function is indicated. Our method should be particularly useful in providing a frame-work in which phenomenological studies of the off-shell pion-nucleon $T$ matrices may be made, since the relationship of our (relativistic) three-dimensional equations to a manifestly covariant theory has been made explicit.