Clusters of galaxies are sites of acceleration of charged particles and sources of non-thermal radiation .
We report on new constraints on the population of cosmic rays in the Intra Cluster Medium ( ICM ) obtained via radio observations of a fairly large sample of massive , X–ray luminous , galaxy clusters in the redshift interval 0.2–0.4 .
The bulk of the observed galaxy clusters does not show any hint of Mpc scale synchrotron radio emission at the cluster center ( Radio Halo ) .
We obtained solid upper limits to the diffuse radio emission and discuss their implications for the models for the origin of Radio Halos .
Our measurements allow us to derive also a limit to the content of cosmic ray protons in the ICM .
Assuming spectral indices of these protons \delta = 2.1 - 2.4 and \mu G level magnetic fields , as from Rotation Measures , these limits are one order of magnitude deeper than present EGRET upper limits , while they are less stringent for steeper spectra and lower magnetic fields .