  The QCD factorization theorem for diffractive processes in DIS is used to
derive formulae for the leading twist contribution to the nuclear shadowing of
parton distributions in the low thickness limit. Based on the current analyzes
of diffraction at HERA we find that the average strength of the interactions
which govern diffraction in the gluon sector at $x \le 10^{-3}, Q_0=2 GeV$ is
~50 mb. This is 3 times larger than in the quark sector and suggests that
applicability of DGLAP approximation requires significantly larger $Q_0$ in the
gluon sector. We use this information to estimate quark and gluon shadowing for
heavy nuclei and to calculate its$Q^2$ depen- dence. For A~200 the amount of
the gluon shadowing: $G_A/AG_N\sim 0.25-0.4$ at $x<10^{-3},Q=2GeV$ is sensitive
to the probability of the small size configurations within wave function of the
gluon "partonometer" at the $Q_0$ scale. At this scale for $A\sim 200$ the
nonperturbative contribution to the gluon density is reduced by a factor of 4-5
at $x \le 10^{-3}$ unmasking PQCD physics in the gluon distribution of heavy
nuclei. Such shadowing would strongly modify the first stage of the heavy ion
collisions at LHC, and would lead to large color opacity effects in $eA$
collisions at x<0.001. The leading twist contribution to the cross section of
the coherent $J/\psi$ production off $A\ge 12$ nuclei at $\sqrt s \ge 70$ GeV
is strongly reduced as compared to the naive color transparency expectations.
The Gribov black body limit for $F_{2A}(x,Q^2)$ is extended to the case of the
gluon distributions in nuclei and shown to be relevant for the HERA kinematics
of $eA$ collisions. Properties of the final states are also briefly discussed.
