  We study the hadron-quark phase transition in the interior of neutron stars
(NS's). We calculate the equation of state (EOS) of hadronic matter using the
Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body
forces, as well as a relativistic mean field model. For quark matter we employ
the MIT bag model constraining the bag constant by using the indications coming
from the recent experimental results obtained at the CERN SPS on the formation
of a quark-gluon plasma. We find necessary to introduce a density dependent bag
parameter, and the corresponding consistent thermodynamical formalism. We
calculate the structure of NS interiors with the EOS comprising both phases,
and we find that the NS maximum masses fall in a relatively narrow interval,
$1.4 M_\odot \leq M_{\rm max} \leq 1.7 M_\odot$. The precise value of the
maximum mass turns out to be only weakly correlated with the value of the
energy density at the assumed transition point in nearly symmetric nuclear
matter.
