The three-body problem with particle absorption and its application to the πd scattering problem

Starting from a set of coupled Schroedinger equations that connect the πNN 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 reversible 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 potentia (OPEP) are naturally induced. 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