Exact solution of a model for πd induced reactions and its application to pion-nucleon reactions

Reduction techniques are applied to πd elastic scattering and π absorption in a theory without anti-nucleons. In the one-pion approximation we derive two sets of exact coupled-channel equations for respectively the amplitudes Tsub(πd,NN), Tsub(NΔ,NN) and Tsub(π,πdsup3) Tsub(πd,NΔ). Alternatively are expressed all amplitudes in terms of the absorption amplitude Tsub(πd,NΔ) and available solutions for a three-body problem restricted to the πd and NΔ channels. It is explicity demonstrated that the model (which comes close to the one of Thomas, Mutzutani and Koltun) strictly respects the Pauli principle and avoids double-counting. Using the same technique amplitudes for the (π,2N) reaction and for π(in) elastic scattering on general nuclei in terms of amplitudes amongst the NN, NNπ channels are determined. Both the elastic amplitude and the πA optical potential are shown to decompose into a multiple scattering part based on an input πN amplitude without the Psub(11) partial wave and calculable absorption corrections. (author)