  Radio observations of a few cool-core galaxy clusters have revealed the
presence of diffuse emission on cluster scales, similar to what was found in
merging clusters in the form of radio halos. These sources might suggest that a
minor merger, while not sufficiently energetic to disrupt the cool core, could
still trigger particle acceleration in the intracluster medium on scales of
hundreds of kpc. We observed with LOFAR at 144 MHz a sample of twelve cool-core
galaxy clusters presenting some level of dynamical disturbances, according to
X-ray data. We also performed a systematic search of cold fronts in these
clusters, re-analysing archival Chandra data. The clusters PSZ1G139.61+24,
A1068 (new detection), MS 1455.0+2232, and RX J1720.1+2638 present diffuse
radio emission on a cluster scale. This emission is characterised by a double
component: a central mini-halo confined by cold fronts and diffuse emission on
larger scales, whose radio power at 144 MHz is comparable to that of radio
halos detected in merging systems. The cold fronts in A1068 are a new
detection. We also found a candidate plasma depletion layer in this cluster. No
sloshing features are found in the other eight clusters. Two of them present a
mini-halo, with diffuse radio emission confined to the cluster core. We also
found a new candidate mini-halo. Whereas, for the remaining five clusters, we
did not detect halo-like emission. For clusters without cluster-scale halos, we
derived upper limits to the radio halo power. We found that cluster-scale
diffuse radio emission is not present in all cool-core clusters when observed
at a low frequency, but it is correlated to the presence of cold fronts. This
morphology requires a specific configuration of the merger and so it puts some
constraints on the turbulence, which deserves to be investigated in the future
with theoretical works.
