  We compute the evolution of the abundances of barium and europium in the
Milky Way and we compare our results with the observed abundances from the
recent UVES Large Program "First Stars". We use a chemical evolution model
which already reproduces the majority of observational constraints. We confirm
that barium is a neutron capture element mainly produced in the low mass AGB
stars during the thermal-pulsing phase by the 13C neutron source, in a slow
neutron capture process. However, in order to reproduce the [Ba/Fe] vs. [Fe/H]
as well as the Ba solar abundance, we suggest that Ba should be also produced
as an r-process element by massive stars in the range 10-30 solar masses. On
the other hand, europium should be only an r-process element produced in the
same range of masses (10-30 solar masses), at variance with previous
suggestions indicating a smaller mass range for the Eu producers. As it is well
known, there is a large spread in the [Ba/Fe] and [Eu/Fe] ratios at low
metallicities, although smaller in the newest data. With our model we estimate
for both elements (Ba and Eu) the ranges for the r-process yields from massive
stars which better reproduce the trend of the data. We find that with the same
yields which are able to explain the observed trends, the large spread in the
[Ba/Fe] and [Eu/Fe] ratios cannot be explained even in the context of an
inhomogeneous models for the chemical evolution of our Galaxy. We therefore
derive the amount by which the yields should be modified to fully account for
the observed spread. We then discuss several possibilities to explain the size
of the spread. We finally suggest that the production ratio of [Ba/Eu] could be
almost constant in the massive stars.
