  In this paper we consider nucleus-nucleus and hadron-nucleus reactions in the
kinematic region: $g A^{1/3} G_{3\pom} \exp\Lb \Delta Y\Rb \approx 1
  G^2_{3\pom} \exp\Lb \Delta Y\Rb \approx 1 $, where $G_{3\pom}$ is the triple
Pomeron coupling, $g$ is the vertex of Pomeron nucleon interaction, and 1 +
$\Delta_{\pom}$ denotes the Pomeron intercept. We find that in this kinematic
region the traditional Glauber-Gribov eikonal approach is inadequate. We show
that it is necesssary to take into account inelastic Glauber corrections, which
can not be expressed in terms of the nucleon-nucleon scattering amplitudes. In
the wide range of energies where $\alpha'_\pom Y
  \ll R^2_A$,the scattering amplitude for the nucleus-nucleus interaction, does
not depend on the details of the nucleon-nucleon interaction at high energy. In
the formalism we present, the only (correlated) parameters that are required to
describe the data are $\Delta_{\pom}$, $G_{3\pom}$ and $g$. These parameters
were taken from our description of the nucleon-nucleon data at high energies
\cite{GLMM}.The predicted nucleus modification factor is compared with RHIC
Au-Au data at $W = 200 GeV.$ Estimates for LHC energies are presented and
discusssed.
