  The quark matter equation of state (EOS) derived from the standard Nambu -
Jona-Lasinio (NJL) model is soft enough to render neutron stars (NS) unstable
at the onset of the deconfined phase, and no pure quark matter can be actually
present in its interior. Since this is a peculiarity of the NJL model, we have
studied a modified NJL model with a momentum cut-off which depends on the
density. This procedure, which improves the agreement between QCD and NJL model
at large density, modifies the standard NJL equation of state, and then it is
potentially relevant for the stability analysis of neutron stars. We show that
also within this approach, the NS instability still persists, and that the
vacuum pressure, as a signal of quark confinement, has a fundamental role for
the NS stability. In this respect, our conclusions point to a relationship
between confinement and NS stability.
