Calculation of the covariant pion-nucleus optical potential. I. Kinematical aspects

Abstract

A discussion of several kinematical schemes used in the study of pion-nucleus scattering is presented. It is shown that various kinematical ambiguities of the noncovariant theories are resolved in a covariant analysis. In particular, the use of an off-mass-shell description for the projectile and the target particles provides a degree of freedom in the kinematical description which avoids various problems present in the noncovariant analyses. We present a comparison of the angle transformations, matrix elements, and differential cross sections obtained from the different kinematical specifications. In these comparisons we have attempted to maintain a clear separation of the dynamical and kinematical assumptions, using the same pion-nucleon interaction in all the cases considered. It is found that the large angle scattering is most sensitive to the details of the kinematical description.