  Ionization feedback should impact the probability distribution function (PDF)
of the column density around the ionized gas. We aim to quantify this effect
and discuss its potential link to the Core and Initial Mass Function (CMF/IMF).
We used in a systematic way Herschel column density maps of several regions
observed within the HOBYS key program: M16, the Rosette and Vela C molecular
cloud, and the RCW 120 H ii region. We fitted the column density PDFs of all
clouds with two lognormal distributions, since they present a double-peak or
enlarged shape in the PDF. Our interpretation is that the lowest part of the
column density distribution describes the turbulent molecular gas while the
second peak corresponds to a compression zone induced by the expansion of the
ionized gas into the turbulent molecular cloud. The condensations at the edge
of the ionized gas have a steep compressed radial profile, sometimes
recognizable in the flattening of the power-law tail. This could lead to an
unambiguous criterion able to disentangle triggered from pre-existing star
formation. In the context of the gravo-turbulent scenario for the origin of the
CMF/IMF, the double peaked/enlarged shape of the PDF may impact the formation
of objects at both the low-mass and the high-mass end of the CMF/IMF. In
particular a broader PDF is required by the gravo-turbulent scenario to fit
properly the IMF with a reasonable initial Mach number for the molecular cloud.
Since other physical processes (e.g. the equation of state and the variations
among the core properties) have already been suggested to broaden the PDF, the
relative importance of the different effects remains an open question.
