Chiral Lagrangians and quark condensate in nuclei

We study the evolution with density of the quark condensate in the nuclear medium with interacting nucleons and including the short-range correlations. We work with two chiral models, the linear sigma model and the non-linear one. For the last one we use two versions, one which does not satisfy PCAC, and another one which does. We show that the quark condensate, as well as the effective pion mass, is independent on the variant selected. The application to physical pions excludes the linear sigma model as a credible one. In the non-linear models our conclusions are the following: (i) There is no systematic reaction imposed by chiral symmetry against symmetry restoration. (ii) The quark condensate evolves essentially linearly with density, as if the nucleons were non-interacting. We examine here one correction due to the two-pion-exchange potential and found it to be negligible. The main correction arises from the one-pion-exchange interaction. (iii) In the s-wave optical potential chiral symmetry tolerates but does not impose two-body terms. On the other hand, the effect of correlations linked to the isospin-symmetric amplitude is negligible.