Nucleon-deuteron scattering with Delta-isobar excitation, - I: Test of separable expansion

A coupled-channel formulation for the description of nucleon-deuteron scatt ering is developed. Three-nucleon channels are coupled to those in which on e nucleon is transformed to a single Delta-isobar. The Delta-isobar is cons idered as a stable baryon with spin and isospin 3/2. The virtual excitation of the Delta-isobar yields an effective three-nucleon force. The three-par ticle scattering equations are solved by a separable expansion of the two-b aryon transition matrix. The validity of the separable expansion is tested in two- and three-nucleon systems. The given separable expansion is shown t o be sufficiently accurate for nucleon-deuteron scattering below the inelas tic threshold of pion production.