Strangeness Production in Light and Intermediate size Nucleus-Nucleus Collisions

Within the statistical model, the net strangeness conservation and incomplete total strangeness equilibration lead to the suppression of strange particle multiplicities. Furthermore, suppression effects appear to be stronger in small systems. By treating the production of strangeness within the canonical ensemble formulation we developed a simple model which allows to predict the excitation function of $K^+/\pi^+$ ratio in nucleus-nucleus collisions. In doing so we assumed that different values of $K^+/\pi^+$, measured in p+p and Pb+Pb interactions at the same collision energy per nucleon, are driven by the finite size effects only. These predictions may serve as a baseline for experimental results from NA61/SHINE at the CERN SPS and the future CBM experiment at FAIR.