Three-pion exchange nucleon-nucleon potentials with virtual Δ -isobar excitation

The nucleon-nucleon interaction arising from the exchange of three pions and the excitation of Δ(1232) isobars in intermediate states is studied. Approximating the Δ propagator by the inverse ΔN mass-splitting, analytical expressions are derived for the spectral functions of the isoscalar and isovector central, spin-spin, and tensor NN potentials in momentum-space. A translation of the spectral functions into coordinate-space potentials reveals that the main effect of these specific exchange and excitation mechanisms is a repulsive isoscalar central NN potential.