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Negatively charged particle with spin 1/2. A component of mundane terrestrial matter, and part of all neutral atoms and molecules. It has a mass about 1/1800 that of a proton. Its antiparticle is the positron.

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"Correlation energy" using the pair correlation function

In case someone else ends up here, here's what I think is going on: As shown in the edit of the question the term containing $g(r)$ gives $E_{el-el}$, the Coulomb energy per particle of the electron- …
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"Correlation energy" using the pair correlation function

In this paper on the Quantum Hall effect the authors refer to something called the correlation energy of electrons. … At this point it is convenient to mention that all this takes place on a sphere; that is the electrons live on a spherical shell at the center of which we have a magnetic Dirac monopole. …