  Nucleus-nucleus scattering is studied in the local Reggeon Field Theory in
the quasi-classical approximation with non-eikonal boundary conditions
corresponding to the Glauber picture at low energies. Comparison with the
commonly used eikonal boundary conditions shows that the new conditions make
both the action and nucleus-nucleus total cross-sections lower by $3\div 5$ %.
They also substantially change the behaviour of the solutions of the equations
of motion at low energies. Using expressions for the double inclusive
cross-sections derived earlier in the Reggeon Field Theory \cite{CM} long-range
rapidity correlations are calculated for the RHIC and LHC energies.
