The Δ potential in nuclear matter from a realistic interaction

Previous studies on the nuclear matter properties have shown the relevance of the Δ isobar degrees of freedom, as well as the need of an accurate estimate of the corresponding Δ potential. Motivated by this result, we have calculated the potential energy of the Δ isobar in nuclear matter with the same model nucleon-nucleon interaction, the Argonne v28, which was previously used in the study of nuclear matter. This potential includes all possible transitions from NN states to NΔ and ΔΔ ones, and give an excellent fit to nucleon-nucleon phenomenological phase shifts and deuteron properties. All diagrams with one nucleon hole-line are summed up in the framework of a G-matrix approach. The Δ potential so obtained was found to be weakly attractive at low density, becoming repulsive at increasing density with a value of 50 MeV at saturation. The repulsive potential receives the main contribution from the isotopic spin T=2 channels and it appears to be in contradiction with the phenomenology on Δ production in nuclei. The sensitivity to possible simple modifications of the potential is explored and it is concluded that complete refitting of the parameters would be necessary in order to remove the contradiction with phenomenology, while keeping the agreement with nucleon-nucleon data. This result indicates the strong constraints that the phenomenology on the Δ isobar imposes on any realistic nucleon-nucleon potential, to be used in self-consistent calculations of nuclear matter properties, which include Δ degrees of freedom. Possible improvements of the interaction are briefly indicated. ((orig.))