Local phenomenological pion-nucleon potentials

Phenomenological local potentials have been widely used to describe the nucleon-nucleon interaction, and many theoretical efforts have been made in order to explain the origin of the various terms in the potential. Contrary to the nucleon-nucleon case, little interest has been shown in local potentials as far as pion-nucleon scattering is concerned. Recent developments in the theory of the 3-body problem have, however, made it worth while to consider local potentials also in the case of 6N scattering. A phenomenological set of such potentials, i.e. one potential for each of the six partial waves that are important at low energies are presented here. These potentials might of course later serve as a meeting ground for phenomenology and calculations based on specific models for the interaction between the particles, just as for the nucleon-nucleon case. The s- and p-wave pion-nucleon scattering phase shifts in the energy region 0-250 MeV are reproduced in a potential model. The potentials are of the soft-core variety and are used in a Klein-Gordon wave equation. (JIW)