Formalism for including the Δ ( 1236 ) resonance in bound trinucleon systems

We present a generalized formulation and angular momentum reduction of the Faddeev equations in momentum space. This permits the consideration of nucleon-isobar configurations generated in the bound trinucleon system through the agency of transition potentials which connect nucleon-nucleon to nucleon-isobar and isobar-isobar two-body states. We show that the exact model equations can be made numerically tractable by dropping small terms in the coupled channel equations and that this then leads to a set of equations not significantly more difficult to solve than the usual Faddeev equations for the nucleon configurations alone. To accomplish this we have carried out a complete angular momentum reduction of the equations which enables us to identify the dominant terms. The procedure can easily be extended, at the cost of more tedious algebra, to allow for the inclusion of the smaller terms, but we believe that the system of equations presented here will account for the major part of the effects of the ..delta.. (1236) resonance in bound trinucleon systems.