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The quark matter equation of state (EOS) derived from the standard Nambu -Jona-Lasinio (NJL) model is soft enough to render neutron stars (NS) unstableat the onset of the deconfined phase, and no pure quark matter can be actuallypresent in its interior. Since this is a peculiarity of the NJL model, we havestudied a modified NJL model with a momentum cut-off which depends on thedensity. This procedure, which improves the agreement between QCD and NJL modelat large density, modifies the standard NJL equation of state, and then it ispotentially relevant for the stability analysis of neutron stars. We show thatalso within this approach, the NS instability still persists, and that thevacuum pressure, as a signal of quark confinement, has a fundamental role forthe NS stability. In this respect, our conclusions point to a relationshipbetween confinement and NS stability.Comment: 5 pages,5 eps figures, title changed, references added, accepted by  Phys. Rev. C (Brief Report

Quark matter in neutron stars within the Nambu-Jona-Lasinio model and confinement