Using the selfconsistent semiclassical Extended Thomas–Fermi (ETF) method up to 4th order in connection with Skyrme forces it is demonstrated that the neutron and proton average potentials obtained using the semiclassical functionals τ(ETF)[ρ] and (ETF)[ρ] reproduce the corresponding Hartree–Fock fields extremely well, except for shell oscillations in the nuclear center.
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