New approach to the theory of coupled πNN-NN systems. (I). Practical equations and unitarity

Starting from a set of coupled Schrödinger equations that connect the π NN and NN systems we arrive at two sets of integral equations which couple physical amplitudes for all relevant processes, namely πd → πd, NN ↔ πd, NN → NN, etc. It is shown explicitly that our theory satisfies two- and three-body unitarity. The rich structure of the two-nucleon interaction above the pion production threshold is discussed, and non-static aspects of the one-pion exchange potential (OPEP) are naturally included. Correct antisymmetrization is worked out so that the theory is compatible with the Pauli principle in all sectors. In their partial wave form, the equations are simple enough to be solved by standard three-body codes. These results allow one to test such effects as the influence of pion absorption on elastic πd scattering, or the importance of the pion production channel in NN processes.