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 $\ensuremath{\pi}N$ scattering based upon current algebra and a dispersion-theoretical axial vector amplitude dominated by the $\ensuremath{\Delta}(1230)$ 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 $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ 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 $\ensuremath{\Delta}(1230)$ $p$-wave resonance.NUCLEAR STRUCTURE Three-body potential; few-nucleon system, Faddeev approach, partial wave decomposition in Jacobi variables.