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Multiple stellar populations in the globular cluster NGC 1851

[Abridged] Detailed chemical tagging of individual stellar populations in the Galactic globular cluster (GC) NGC 1851 is presented. Abundances are derived from FLAMES spectra for the largest sample of giants (124) ever analysed in this peculiar GC using O, Na, Mg, Al, Si, Ca, Ti, Sc, V, Mn, Co, Ni, Cu, Y, Zr, Ba, La, Ce, Nd, Eu, Dy. We confirm a [Fe/H] spread in this GC, but too small to clearly separate different sub-populations. We instead propose a classification using a combination of Fe and Ba (much more abundant in the more metal-rich group) through a cluster analysis: we separated stars into a metal-rich (MR) and a metal-poor (MP) populations, each of them showing a Na-O anticorrelation, signature of genuine GC, although with different ratios of primordial to polluted stars. The ratio [alpha/H] tracks iron and is higher in the MR population, suggesting an additional contribution by core-collapse supernovae. The MR population shows a larger enrichment in s-process elements compared to the MP one. This is probably due to the contribution by intermediate-low mass stars, because we find that the level of heavy s-process elements is larger than the level of light s-process nuclei in the MR stars; however, a large contribution by low mass stars is unlikely, because it would likely cancel the O-Na anticorrelation. We also confirm the presence of correlations between p-capture and s-process elements previously found by other studies, at least for the MR population. This finding apparently requires a quite long delay for the second generation of the MR component. A merger of two distinct GCs in a parent dwarf galaxy, each one with a different Ba level and an age difference of ~1 Gyr, might explain (i) the double SGB, (ii) a possible difference in C content between the two original GCs, and (iii) the Stromgren photometry of this peculiar GC.