We present the complete momentum space three-nucleon potential of the two-pion-exchange type in the partial wave decomposition needed for the Faddeev equations of the three-nucleon bound state. The potential arises from an off-mass-shell model for $\pi N$ scattering based upon current algebra and a dispersion-theoretical axial vector amplitude dominated by the $\Delta \mathrm{}\left(1230\right)\mathrm{}$ isobar. The potential is manifestly Hermitian and defined for all three nucleon momenta. We display some matrix elements of the potential in the five three-body partial waves corresponding to the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ states of the two-body subsystem. These matrix elements show a striking contrast to those of an older three-body potential mediated only by the $\Delta \mathrm{}\left(1230\right)\mathrm{}$ $p$-wave resonance.

NUCLEAR STRUCTURE Three-body potential; few-nucleon system, Faddeev approach, partial wave decomposition in Jacobi variables.

• Received 18 March 1980

DOI:https://doi.org/10.1103/PhysRevC.23.1790