The structure of high density nuclear matter is studied in the framework of a new approach, a mean-field description of non-overlapping neutron and proton bags with soft surfaces bound by the self-consistent exchange of the , and meson fields. We consider in this formulation each bag with an internal region, where quarks are free, a finite surface region, where the quark wave functions are gradually suppressed, and an exterior region, where the quark wave functions vanish. The finite surface region with a typical scale of about half a Fermi models the smooth transition region between the perturbative and non-perturbative vacua, as expected from a gradual outside-inside restoration of chiral symmetry. As an application we determine the structure of the equation of state for neutron stars. We then consistently include in the formulation lepton degrees of freedom, the chemical equilibrium conditions for neutron stars and baryon number and electric charge conservation. We investigate properties of both nuclear and neutron matter. Using the TOV equations, the role of the softness of quark bags degrees of freedom on bulk static properties of neutron stars are determined.
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