Nuclei energy functional for

We consider here the example of the Skyrme energy functional where the potential energy is modeled as 

One more difference from the electronic case needs finally to be remarked. The functional (3) parameterizes the mean-field for two sorts of fermions, namely neutrons and protons. This introduces one more distinctive quantum number, the isospin. Correspondingly, we see isoscalar (T = 0) terms p = pp + p , and isovector (T = 1) terms, 8p = Pn — Pp. Both together provide a complete description of nuclei. In metals, on the other hand, we have only the Fermi liquid of (valence) electrons. But there come in addition the ions as partner constituents that need to be modeled additionally, e.g. by pseudopotentials or by the jellium approach. And there is a large variety of ionic backgrounds corresponding to the overwhelming variety of materials. 

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