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IThe possibility of abnormally occupying plane-wave Hartree-Fock determinants is studied analytically for several many-fermion systems interacting with shortand long-ranged pair potentials in three dimensions. Lower energy states are found in some cases, but they always depend sensitively on the shape of the potential as well as on the amount of space exchange present in the interaction. jNUCLEAB STRUCTURE Plane-wave Hartree-Fock, nuclear matter. ]