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A recently introduced analytical model for the nuclear density profile[1] isimplemented in the Extended Thomas-Fermi (ETF) energy density functional.  This allows to (i) shed a new light on the issue of the sign of surfacesymmetry energy in nuclear mass formulas, which is strongly related to thenon-uniformity of the isospin asymmetry in finite nuclei, as well as to (ii)evaluate the in-medium corrections to the nuclear cluster energies inthermodynamic conditions relevant for the description of the (proto)-neutronstar crust. The ground state configurations of the model are compared toHartree-Fock calculations in spherical symmetry for some selected isotopicchains, and systematic errors are quantified. The in-medium modification of thenuclear mass due to the presence of a gas component is shown to strongly dependboth on the density and the asymmetry of the nucleon gas. This shows theimportance of accounting for such effects in the realistic modelizations of theequation of state for core-collapse supernovae and proto-neutron stars.

In-medium nuclear cluster energies within the Extended Thomas-Fermi approach