${\mathrm{\Delta }}_{33}$-isobar contribution to the soft nucleon-nucleon potentials. II. πρ-exchange potentials

Pion-rho-exchange nucleon-nucleon potentials are derived for one or two Δ isobars in the intermediate states. As in the companion work on two-pion exchange, strong dynamical pair suppression is assumed. At the NNπ, ρ and NΔπ, ρ vertices Gaussian form factors are incorporated into the relativistic two-body framework by using a dispersion representation for the π- and ρ-exchange amplitudes. The Fourier transformations are performed using factorization techniques for the energy denominators, taking into account the mass difference between the nucleon and the Δ isobar. The potentials are calculated in the adiabatic approximation of all planar and crossed three-dimensional momentum-space πρ diagrams. We also give the contributions of the πρ iteration, which can be subtracted or not, depending on whether one performs a coupled-channel calculation for, e.g., the NN, NΔ system, or a single NN-channel calculation.