  We report on the discovery of a surprising observed correlation between the
slope of the low-mass stellar global mass function (GMF) of globular clusters
(GCs) and their central concentration parameter c=log(r_t/r_c), i.e. the
logarithmic ratio of tidal and core radii. This result is based on the analysis
of a sample of twenty Galactic GCs with solid GMF measurements from deep HST or
VLT data. All the high-concentration clusters in the sample have a steep GMF,
most likely reflecting their initial mass function. Conversely,
low-concentration clusters tend to have a flatter GMF implying that they have
lost many stars via evaporation or tidal stripping. No GCs are found with a
flat GMF and high central concentration. This finding appears
counter-intuitive, since the same two-body relaxation mechanism that causes
stars to evaporate and the cluster to eventually dissolve should also lead to
higher central density and possibly core-collapse. Therefore, more concentrated
clusters should have lost proportionately more stars and have a shallower GMF
than low concentration clusters, contrary to what is observed. It is possible
that severely depleted GCs have also undergone core collapse and have already
recovered a normal radial density profile. It is, however, more likely that GCs
with a flat GMF have a much denser and smaller core than suggested by their
surface brightness profile and may well be undergoing collapse at present. In
either case, we may have so far seriously underestimated the number of post
core-collapse clusters and many may be lurking in the Milky Way.
