The determination of the Ba abundance in globular cluster (GC) stars is a very powerful test to address several issues in the framework of multiple population scenarios. We measured the Ba content for a sample of more than 1200 stars in 15 Galactic GCs, using high-resolution FLAMES/Giraffe spectra. We found no variation in [Ba/Fe] ratios for different stellar populations within each cluster; this means that low-mass asymptotic giant branch stars do not significantly contribute to the intracluster pollution. Very interestingly, we found that the fraction of Ba stars in first generation (FG) stars is close to the values derived for field stars (∼2%); on the other hand, second generation (SG) stars present a significantly lower fraction. An independent and successful test, based on radial velocity variations among giant stars in NGC 6121, confirms our finding: the binary fraction among FG stars is about ∼12%, to be compared with ∼1% of SG stars. This is an evidence that SG stars formed in a denser environment, where infant mortality of binary systems was particularly efficient.