We evaluate the Cronin effect in pA collisions at the CERN LHC and at RHIC in the framework of Glauber-eikonal model of initial state multiparton interactions. Taking carefully into account all kinematical constraints of each multi-parton interaction process we obtain a softening of the spectrum of produced partons, improving in this way the agreement of the model with the recent measurements of \pi 0 production in d+Au collisions at \sqrt s=200 AGeV.
PACS numbers: 24.85+p, 11.80.La, 25.75.--q
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