Three-body force in nuclear matter from ππ-, πp-, and pp-exchanges

We derive, in the static approximation, the 2π-, πrho - and 2rho- exchange - 3N forces mediated by the Δ (1232 MeV) resonance treated as a Rarita-Schwinger particle. The contribution of these 3N potentials to the binding energy of the infinite medium is estimated by a standard nuclear matter calculation of first order in the Bruckner G matrix. We find that the inclusion of the πrho - and 2 rho 3N forces reduces the attraction obtained with the 2π 3N force alone. In contrast with earlier studies with the 2π 3N potential using a long ranged monopole form factor of mass etasub(π) = 0.44 GeV, we use medium ranged ones of masses etasub(π) = 1 to 1.3 GeV and etasub(rho) = 1.3 to 1.7 GeV. These values are consistent with those considered in Nucleon-Nucleon scattering and some other nuclear problems. We obtain a repulsive and saturating effect which could be very strong depending on the rho NN and rho N Δ coupling. For instance we get a repulsion of 6.7 MeV at ksub(F) = 1.36 fm-1 in the strong rho coupling case with etasub(π) = 1 GeV and etasub(rho) = 1.3 GeV. Adding a 2π 3N component coming from πN S-wave scattering would reduce somewhat this repulsion which might also be partly cancelled by some other 3 π-exchange - 3N forces. (orig.)