  We show an interesting correlation between the surface brightness and
temperature structure of the relaxed clusters RXJ1720.1+2638 and MS1455.0+2232,
hosting a pair of cold fronts, and their central core--halo radio source. We
discuss the possibility that the origin of this diffuse radio emission may be
strictly connected with the gas sloshing mechanism suggested to explain the
formation of cold fronts in non major merging clusters. We show that the
radiative lifetime of the relativistic electrons is much shorter than the
timescale on which they can be transported from the central galaxy up to the
radius of the outermost cold front. This strongly indicates that the observed
diffuse radio emission is likely produced by electrons re--accelerated via some
kind of turbulence generated within the cluster volume limited by the cold
fronts during the gas sloshing.
