  A renewed interest about the origin of \emph{r}-process elements has been
stimulated by the multi-messenger observation of the gravitational event
GW170817, with the detection of both gravitational waves and electromagnetic
waves corresponding to the merger of two neutron stars. Such phenomenon has
been proposed as one of the main sources of the \emph{r}-process. However, the
origin of the \emph{r}-process elements at different metallicities is still
under debate. We aim at investigating the origin of the \emph{r}-process
elements in the Galactic thin disc population. From the sixth internal data
release of the \emph{Gaia}-ESO we have collected a large sample of Milky Way
thin- and thick-disc stars for which abundances of Eu, O, and Mg are available.
The sample consists of members of 62 open clusters, located at a Galactocentric
radius from $\sim 5$ kpc to $\sim 20$ kpc in the disc, in the metallicity range
$[-0.5, 0.4]$ and covering an age interval from 0.1 to 7 Gy, and about 1300
Milky Way disc field stars in the metallicity range $[-1.5, 0.5]$. We compare
the observations with the results of a chemical evolution model, in which we
varied the nucleosynthesis sources for the three considered elements. Our main
result is that Eu in the thin disc is predominantly produced by sources with
short lifetimes, such as magneto-rotationally driven SNe. There is no strong
evidence for additional sources at delayed times. Our findings do not imply
that there cannot be a contribution from mergers of neutron stars in other
environments, as in the halo or in dwarf spheroidal galaxies, but such a
contribution is not needed to explain Eu abundances at thin disc metallicities.
