Semi-classical methods of statistical mechanics can incorporate essentialquantum effects by using effective quantum potentials. An ideal Fermi gasinteracting with an impurity is represented by a classical fluid with effectiveelectron-electron and electron-impurity quantum potentials. Theelectron-impurity quantum potential is evaluated at weak coupling, leading to ageneralization of the Kelbg potential to include both diffraction anddegeneracy effects. The electron-electron quantum potential for exchangeeffects only is the same as that discussed earlier by others.
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