  Context. Thanks to the heroic observational campaigns carried out in recent
years we now have large samples of metal-poor stars for which measurements of
detailed abundances exist. [...] These data hold important clues on the nature
of the contribution of the first stellar generations to the enrichment of our
Galaxy. Aims. We aim to explain the scatter in Sr, Ba, Y, and Eu abundance
ratio diagrams unveiled by the metal-poor halo stars. Methods. We computed
inhomogeneous chemical evolution models for the Galactic halo assuming
different scenarios for the r-process site: the electron-capture supernovae
(EC) and the magnetorotationally driven (MRD) supernovae scenario. We also
considered models with and without the contribution of fast-rotating massive
stars (spinstars) to an early enrichment by the s-process. A detailed
comparison with the now large sample of stars with measured abundances of Sr,
Ba, Y, Eu, and Fe is provided (both in terms of scatter plots and number
distributions for several abundance ratios). Results. The scatter observed in
these abundance ratios of the very metal-poor stars (with [Fe/H] < -2.5) can be
explained by combining the s-process production in spinstars, and the r-process
contribution coming from massive stars. For the r-process we have developed
models for both the EC and the MRD scenario that match the observations.
Conclusions. With the present observational and theoretical constraints we
cannot distinguish between the EC and the MRD scenario in the Galactic halo.
Independently of the r-process scenarios adopted, the production of elements by
an s-process in spinstars is needed to reproduce the spread in abundances of
the light neutron capture elements (Sr and Y) over heavy neutron capture
elements (Ba and Eu). We provide a way to test our suggestions by means of the
distribution of the Ba isotopic ratios in a [Ba/Fe] or [Sr/Ba] vs. [Fe/H]
diagram.
