To understand the formation and evolution of the different stellar populations within our Galaxy it is essential to combine detailed kinematical and chemical information for large samples of stars. We derive chemical abundances of Cu, Zn, Sr, Y, Zr, Ba, Ce, Nd and Eu for a large sample of more than 1000 FGK dwarf stars with high-resolution ($R sim$,115000) and high-quality spectra from the HARPS-GTO program. The abundances are derived by a standard Local Thermodinamyc Equilibrium (LTE) analysis using measured Equivalent Widths (EWs) injected to the code MOOG and a grid of Kurucz ATLAS9 atmospheres. We find that thick disk stars are chemically disjunct for Zn and Eu and also show on average higher Zr but lower Ba and Y when compared to the thin disk stars. We also discovered that the previously identified high-$alpha$ metal-rich population is also enhanced in Cu, Zn, Nd and Eu with respect to the thin disk but presents Ba and Y abundances lower on average, following the trend of thick disk stars towards higher metallities and further supporting the different chemical composition of this population. The ratio of heavy-s to light-s elements of thin disk stars presents the expected behaviour (increasing towards lower metallicities) and can be explained by a major contribution of low-mass AGB stars for s-process production at disk metallicities. However, the opposite trend found for thick disk stars suggests that intermediate-mass AGB stars played an important role in the enrichment of the gas from where these stars formed. Previous works in the literature also point to a possible primary production of light-s elements at low metallicities to explain this trend. Finally, we also find an enhancement of light-s elements in the thin disk at super solar metallicities which could be caused by the contribution of metal-rich AGB stars. (short version)