  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.
