Charge Screening at First Order Phase Transitions and Hadron - Quark Mixed Phase

Possibility of structured mixed phases at first order phase transitions in neutron stars is re-examined by taking into account charge screening and surface effects. Transition from the hadron $npe$ phase to the quark phase is studied. Two possibilities, the mixed phase and two separate phases given by the double-tangent (Maxwell) construction are considered. Inhomogeneous profiles of the electric potential and their contribution to the energy are analytically calculated. The electric field configurations determine the droplet size and the geometry of structures.

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