π- and ϱ-exchange three-nucleon potentials (I)

The current algebra program of the ππ exchange three-body force (TBF) is extended to include ϱ- and π-meson exchange. A qualitative discussion is given of the origin of the potentials which are constrained by the low-energy theorems of Thirring, Beg, and Kroll and Ruderman and supplemented by Δ-isobar contributions. The leading local parts of the ϱϱ and ϱπ TBF's are presented and used to estimate the binding energy of nuclear matter. The contributions are ππ TBF ∼- −4 MeV , ϱπ TBF ∼- +2 MeV , ϱϱ TBF ∼- − 1 4 MeV . The relative contributions from model-independent low-energy theorems and from the Δ-isobar to the ϱπ and ρρ potentials are discussed. In contrast to the ππ exchange TBF which is dominated by the model-independent part, the ϱπ and pp potentials have substantial contributions from an explicit Δ-isobar. The convergence of the nuclear matter estimates with respect to exchanged meson mass indicates that future calculations should not be concerned with heavier meson exchanges. The form factors used in the estimates with these potentials are collected in an appendix.