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 ($\sigma$ 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.