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

Nucleus-nucleus cross-sections and long-range correlations with a local supercritical pomeron