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The recently developed "internal" Density Functional Theory provides anexistence theorem for a local potential that contains the center-of-masscorrelations effects. The knowledge of the corresponding energy functionalwould provide a much cheaper way than projection techniques to treat thesecorrelations. The aim of this article is to construct such a functional. Wepropose a well-founded method, suitable for Fermions as well as for Bosons,which does not require any free parameters.

An alternate well-founded way to treat the center-of-mass correlations: use of a local center-of-mass correlations potential