Wigner-Seitz radius

The Wigner–Seitz radius ${\displaystyle r_{s}}$, named after Eugene Wigner and Frederick Seitz, is the radius of a sphere whose volume is equal to the mean volume per atom in a solid (for first group metals). In the more general case of metals having more valence electrons, ${\displaystyle r_{s}}$ is the radius of a sphere whose volume is equal to the volume per a free electron. This parameter is used frequently in condensed matter physics to describe the density of a system. Worth to mention, ${\displaystyle r_{s}}$ is calculated for bulk materials.

In a 3-D system with ${\displaystyle N}$ free electrons in a volume ${\displaystyle V}$, the Wigner–Seitz radius is defined by

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