Properties of a proto-neutron star with smeared trapped neutrinos

We investigate the structure of a proto-neutron star with trapped neutrinos by using quantum hadrodynamics. Ratios of the trapped neutrinos and corresponding leptons to the baryons are usually assumed to be constant. But relevant reactions associated with the β equilibrium could be sensitive to the given density and temperature. By adopting a phenomenological lepton density that is smeared near the surface, we calculate and discuss populations of baryons and leptons, equations of state, and the mass-radius relation of a proto-neutron star in an isentropic process.