Two-pion-exchange three-nucleon potential: Partial wave analysis in momentum space

Abstract

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.