The Gaia-ESO survey: the non-universality of the
  age-chemical-clocks-metallicity relations in the Galactic disc
  In the era of large spectroscopic surveys, massive databases of high-quality
spectra provide tools to outline a new picture of our Galaxy. In this
framework, an important piece of information is provided by our ability to
infer stellar ages. We aim to provide empirical relations between stellar ages
and abundance ratios for a sample of solar-like stars. We investigate the
dependence on metallicity, and we apply our relations to Gaia-ESO samples of
open clusters and field stars. We analyse high-resolution and high-S/N HARPS
spectra of a sample of solar-like stars to obtain precise determinations of
their atmospheric parameters and abundances through differential spectral
analysis and age through isochrone fitting. We investigate the relations
between ages and abundance ratios. For the abundance ratios with a steeper
dependence on age, we perform multivariate linear regressions, including the
dependence on metallicity. We apply our relations to a sample of open clusters
located in 4<R$_{GC}$<16 kpc. Using them, we are able to recover the literature
ages only for clusters located at R$_{GC}$>7 kpc. In these clusters, the
content of s-elements is lower than expected from chemical evolution models,
and consequently the [s/$\alpha$] are lower than in clusters of the same age
located in the solar neighbourhood. With our chemical evolution model and a set
of empirical yields, we suggest that a strong dependence on the star formation
history and metallicity-dependent yields of s-elements can substantially modify
the slope of the [s/$\alpha$]-[Fe/H]-age relation in different regions of the
Galaxy. Our results point towards a non-universal relation
[s/$\alpha$]-[Fe/H]-age, indicating the existence of relations at different
R$_{GC}$ or for different star formation history. A better understanding of the
s-process at high metallicity is necessary to fully understand the origin of
these variations.
