Two pion mediated scalar isoscalar NN interaction in the nuclear medium

We study the modification of the nucleon-nucleon interaction in a nuclear medium in the scalar isoscalar channel, mediated by the exchange of two correlated (σ channel) or uncorrelated pions. For this purpose we use a standard approach for the renormalization of pions in nuclei. The corrections obtained for the NN interaction in the medium in this channel are of the order of 20% of the free one in average, and the consideration of short-range correlations plays an important role in providing these moderate changes. Yet, the corrections are sizable enough to suggest further studies of the stability and properties of nuclear matter