Critical fluctuations of the quark density in nuclei

We study the static scalar susceptibility of the nuclear medium, i.e., the change of the quark condensate for a small modification of the quark mass.In the linear sigma model it is linked to the in-medium sigma propagator.Near the critical density for the chiral phase transition it becomes large, reflecting the presence of large spontaneous fluctuations of the quark scalar density. A partial access to this phenomenon is provided by the nuclear response for probes which couple to the nucleon density fluctuations. We show that such probes experience a critical scattering, i.e., an anomalous scattering in the forward direction. The data on the longitudinal response in (e.e') scattering support the existence of this phenomenon at normal nuclear densities.