Context : A complete set of orbital parameters for barium stars , including the longest orbits , has recently been obtained thanks to a radial-velocity monitoring with the HERMES spectrograph installed on the Flemish Mercator telescope .
Barium stars are supposed to belong to post-mass-transfer systems .

Aims : In order to identify diagnostics distinguishing between pre- and post-mass-transfer systems , the properties of barium stars ( more precisely their mass-function distribution and their period – eccentricity ( P - e ) diagram ) are compared to those of binary red giants in open clusters .
As a side product , we aim to identify possible post-mass-transfer systems among the cluster giants from the presence of s -process overabundances .
We investigate the relation between the s -process enrichment , the location in the ( P - e ) diagram , and the cluster metallicity and turn-off mass .

Methods : To invert the mass-function distribution and derive the mass-ratio distribution , we used the method pioneered by Boffin et al .
( 1992 ) that relies on a Richardson-Lucy deconvolution algorithm .
The derivation of s -process abundances in the open-cluster giants was performed through spectral synthesis with MARCS model atmospheres .

Results : A fraction of 22 % of post-mass-transfer systems is found among the cluster binary giants ( with companion masses between 0.58 and 0.87 M _ { \odot } , typical for white dwarfs ) , and these systems occupy a wider area than barium stars in the ( P - e ) diagram .
Barium stars have on average lower eccentricities at a given orbital period .
When the sample of binary giant stars in clusters is restricted to the subsample of systems occupying the same locus as the barium stars in the ( P - e ) diagram , and with a mass function compatible with a WD companion , 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 ) .
The only strong barium star in our sample is found in the cluster with the lowest metallicity in the sample ( i.e .
star 173 in NGC 2420 , with [ Fe/H ] = -0.26 ) , whereas the barium stars with mild s -process abundance anomalies ( from 0.25 to \sim 0.6 dex ) are found in the clusters with slightly subsolar metallicities .
Our finding confirms the classical prediction that the s -process nucleosynthesis is more efficient at low metallicities , since the s -process overabundance is not clearly correlated with the cluster turn-off ( TO ) mass ; such a correlation would instead hint at the importance of the dilution factor .
We also find a mild barium star in NGC 2335 , a cluster with a large TO mass of 4.3 M _ { \odot } , which implies that asymptotic giant branch stars that massive still operate the s -process and the third dredge-up .

Conclusions :