  We recently performed a study of a sample of relaxed, cooling core galaxy
clusters with deep Very Large Array observations at 1.4 GHz. We find that in
the central regions of A1835, A2029, and Ophiuchus the dominant radio galaxy is
surrounded by a diffuse low-brightness radio emission that takes the form of a
mini-halo. Here we present the results of the analysis of the extended diffuse
radio emission in these mini-halos. In order to investigate the morphological
properties of the diffuse radio emission in clusters of galaxies we propose to
fit their azimuthally averaged brightness profile with an exponential,
obtaining the central brightness and the e-folding radius from which the radio
emissivity can be calculated. We investigate the radio properties of the
mini-halos in A1835, A2029, and Ophiuchus in comparison with the radio
properties of a representative sample of mini-halos and halos already known in
the literature. We find that radio halos can have quite different length-scales
but their emissivity is remarkably similar from one halo to the other. In
contrast, mini-halos span a wide range of radio emissivity. Some of them, like
the Perseus mini-halos, are characterized by a radio emissivity which is more
than 100 times greater than that of radio halos. On the other hand, the new
mini-halos in cooling core clusters analyzed in this work, namely A2029,
Ophiuchus, and A1835, have a radio emissivity which is much more typical of
halos in merging clusters rather than similar to that of the other mini-halos
previously known.
