  The Halo Galactic Globular Clusters (GCs) lying inside the solar circle
(\inn, \r $< 8 Kpc$, \feh$<-0.8$) are shown to keep no record of the strong
correlation between GC absolute integrated magnitudes and core parameters
(concentration and central density) clearly detected for the Halo GCs lying
outside this circle (\out) as well as (at lower statistical significance) for
those belonging to the \dis population ($\feh >-0.8$). We present here both
observational evidences and theoretical simulations supporting the hypothesis
of a {\it primordial} origin for such correlations and of an {\it
environment-induced} destruction of them if absent. In particular, this
hypothesis lead us to argue that \inn Halo GCs have undergone a chaotic,
environment-driven, dynamical evolution not shared by the \dis GCs though the
radial zone of the Galaxy occupied by the two groups is nearly the same.
