In order to identify diagnostics distinguishing between pre- and post-mass-transfer systems, the mass-ratio distribution and period - eccentricity (P - e) diagram of barium and S stars are compared to those of the sample of binary red giants in open clusters from Mermilliod et al. (2007). From the analysis of the mass-ratio distribution for the cluster binary giants, we find an excess of systems with companion masses between 0.58 and 0.87 Msun, typical for white dwarfs. They represent 22% of the sample, which are thus candidate post-mass-transfer systems. Among these candidates which occupy the same locus as the barium and S stars in the (P-e) diagram, only 33% (= 4/12) show a chemical signature of mass transfer in the form of s-process overabundances (from rather moderate -- about 0.3 dex -- to more extreme -- about 1 dex). These s-process-enriched cluster stars show a clear tendency to be in the clusters with the lowest metallicity in the sample, confirming the classical prediction that the s-process nucleosynthesis is more efficient at low metallicities (the only strong barium star in our sample is found in the cluster with the lowest metallicity, i.e., star 173 in NGC 2420, with [Fe/H] = -0.26). The s-process overabundance is not clearly correlated with the cluster turnoff (TO) mass (such a correlation would instead hint at the importance of the dilution factor). We find as well a mild barium star in NGC 2335, a cluster with a large TO mass of 4.3 Msun, which implies that intermediate-mass AGB stars still operate the s-process and the third dredge-up.
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