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Clear up some confusion regarding the rs parameter. |
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:<math>\epsilon_{c} = \frac{1}{2}\left(\frac{g_{0}}{r_{s}} + \frac{g_{1}}{r_{s}^{3/2}} + \dots\right)\ ,</math>
where the Wigner-Seitz parameter <math>r_{s}</math> is dimensionless. <ref>{{cite journal | title = Correlation Energy of an Electron Gas at High Density | author = Murray Gell-Mann and Keith A. Brueckner | journal = Phys. Rev. | volume = 106 | pages = 364 | year = 1957 | doi = 10.1103/PhysRev.106.364 | issue = 2}}</ref> It is defined as the radius of a sphere which encompasses exactly one electron, divided by the Bohr radius. The Wigner-Seitz parameter <math>r_s</math> is related to the density as
:<math>\frac{4}{3}\pi r_{s}^{3} = \frac{1}{\rho}\ .</math>
The analytical expression for the full range of densities has been proposed based on the many-body perturbation theory. The error as compared to the near-exact [[quantum Monte Carlo]] simulation is on the order of milli-Hartree.
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