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Neutron-skins in coordinate space and proton-skins in momentum space arepredicted to coexist in heavy nuclei and their correlation is governed byLiouville's theorem and Heisenberg's uncertainty principle. An analysis oftheir correlation within a further extended Thomas-Fermi (ETF$^+$)approximation incorporating effects of nucleon short-range correlations revealsgenerally that protons move faster than neutrons in neutron-skins of heavynuclei.

Proton-skins in momentum space and neutron-skins in coordinate space in heavy nuclei