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=200GeV. Estimates for LHC energies are presented and
discusssed.Comment: 18pp. 14 fugure