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The repulsive hard core of a pair-wise interaction acting between fermions is simulated by a constraint to be included in the variational principle. The Euler-Lagrange equations are usual Hartree-Fock equations with a self-consistent one-body pseudopotential. It can be seen that the imposed constraint generates a correlation field in addition to the regular portion of the two-body interaction. The origin of density waves in coordinate space is discussed in terms of the hard-core correlations.

Self-consistent pseudopotentials in the thermodynamic limit. I. The correlation field