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The nucleon-nucleon interaction arising from the exchange of three pions andthe excitation of $\Delta(1232)$-isobars in intermediate states is studied.Approximating the $\Delta$-propagator by the inverse $\Delta$N mass-splitting,analytical expressions are derived for the spectral-functions of the isoscalarand isovector central, spin-spin and tensor NN-potentials in momentum-space. Atrans- lation of the spectral-functions into coordinate-space potentialsreveals that the main effect of these specific exchange and excitationmechanisms is a repulsive isoscalar central NN-potential.

Three-pion exchange nucleon-nucleon potentials with virtual $\Delta$-isobar excitation