The role of the Δ in nuclear physics

We review the properties of Δ, and the role it plays in Nuclear Physics. We try to assess what has been ascertained up to now, and what remains to be clarified about this hadron, which represents the outstanding structure in the medium-energy pion–nucleon interaction. We consider the free Δ first, with particular emphasis on those aspects which may give information on the internal hadron structure, such as the isospin mass splittings in the Δ multiplet, and the electromagnetic fingerprints of deviation from spherical symmetry. We then discuss the N–Δ interaction, both under the point of view of meson-exchange models, and under a microscopic quark-model perspective. In so doing, we review the present status of the meson–nucleon and meson–Δ coupling constants and form factors, whose knowledge is a prerequisite for a description of nuclei in terms of effective hadronic degrees of freedom. We discuss also the coupled-channel approach to the NN–NΔ system, and how it compares with relativistic treatments grounded on Quantum Field Theory. We then consider light nuclei, where the percentage of Δ components in the nuclear wave function, and Δ contributions to meson-exchange currents can be studied in a quantitative way, with a minimum of uncertainties due to nuclear-structure effects. Finally, we discuss Δ propagation in finite nuclei and nuclear matter. To this end, we try to give an update presentation of classical subjects, such as the effective Δ interaction in the nuclear environment, medium effects and quenching phenomena, where Δ-hole excitations and nuclear-structure effects are strictly intertwined.