Statistical Theory of the Atom in Momentum Space

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We investigate a semiclassical momentum density energy functional for atoms and show that it yields the same value as the well-known Thomas-Fermi functional. In fact, we show an explicit relation between the minimizers of the two functionals. The main result is that the atomic momentum density converges on the scale Z²/³ to the minimizer of the momentum density energy functional. This allows to determine the linear response of atoms on momentum dependent perturbations.