  We study the evolution of the [Eu/Fe] ratio in the Galactic halo by means of
a stochastic chemical evolution model considering merging neutron stars as
polluters of europium. We improved our previous stochastic chemical evolution
model by adding a time delay distribution for the coalescence of the neutron
stars, instead of constant delays. The stochastic chemical evolution model can
reproduce the trend and the observed spread in the [Eu/Fe] data with neutron
star mergers as unique producers if we assume: i) a delay time distribution
$\propto t^{-1.5}$, ii) a $M_{Eu}= 1.5$x$10^{-6} M_{\odot}$ per event, iii)
progenitors of neutron stars in the range $9-50M_{\odot}$ and iv) a constant
fraction of massive stars in the initial mass function (0.02) that produce
neutron star mergers. Our best model is obtained by relaxing point iv) and
assuming a fraction that varies with metallicity. We confirm that the mixed
scenario with both merging neutron stars and supernovae as europium producers
can provide a good agreement with the data relaxing the constraints on the
distribution time delays for the coalescence of neutron stars. Adopting our
best model, we also reproduce the dispersion of [Eu/Fe] at a given metallicity,
which depends on the fraction of massive stars that produce neutron star
mergers. Future high-resolution spectroscopic surveys, such as 4MOST and WEAVE,
will produce the necessary statistics to constrain at best this parameter.
