Two-pion exchange and chiral symmetry restoration

The scalar, isoscalar piece of the two-pion exchange force between two nucleons is calculated in the linear σ model. A large contribution to this force is found to come from terms involving direct coupling of the σ field to the nucleons. This part of the interaction can be related to the partial restoration of chiral symmetry experienced by a nucleon in nuclear matter, and it has a strength determined by the σ commutator. Even if the ‘‘elementary’’ σ is taken to be heavy (${\mathit{m}}_{\mathrm{\sigma }}$>1GeV), the effect has a longer range, determined by the mass of the pair of pions. Although the σ fields used in relativistic models of nuclei have a similar strength and range, no simple relationship is found between such fields and partial restoration of chiral symmetry.