Relativistic three-body approach to NN scattering at intermediate energies

The Bethe-Salpeter equation for coupled-channel N-Δ scattering is extended to satisfy unitarity in the NN and NNπ sectors. The procedure eliminates the unitarity violations characteristic of the standard ladder Bethe-Salpeter equation in the inelastic region, and improves the description of pion production near threshold. Results are presented for the NN phase shifts and a number of observables up to 1 GeV. In particular, the ${}_{}{}^1{}_{}{}^{}\mathrm{D}_2^{}{}_{}{}^{}$ inelasticity is found to be considerably smaller than found from phase shift analysis. In this context, the importance of the pion deuteron channel for the inelasticity parameter is pointed out.