Deviations from the superposition model in a Dual Parton Model with formation zone cascade in both projectile and target nuclei

A Dual Parton Model with a formation zone intranuclear cascade in the spectators of the projectile and target nuclei is studied. The hadrons produced in the formation zone cascade contribute to Feynman-$x_F$ and lab-$x$ distributions in the fragmentation regions of the target and projectile nuclei. We discuss the consequences of this model in the secondary cosmic ray production, by analyzing the calculated spectrum weighted moments for pion and kaon production. We show that the proposed model leads to significant differences with respect to a simple superposition model, where the nucleus-nucleus collision is replaced by a few corresponding nucleon-nucleus collisions.