Wigner-Seitz radius

The Wigner–Seitz radius, denoted $r\_s$, is a parameter used frequently in condensed matter physics to describe the density of a system. If the total volume "V" of a system (assuming 3-D) is equally divided amongst "N" particles (normally valence electrons), then the volume occupied by each particle is simply

:$v\; =\; frac\{4\}\{3\}\; pi\; r\_s^3$.

Solving for $r\_s$ we obtain

:$r\_s\; =\; left(frac\{3v\}\{4pi\}\; ight)^\{1/3\}$,

where $v\; =\; frac\{V\}\{N\}$.

This parameter is normally reported in atomic units. For a non-interacting system, the average separation between two particles will be $2\; r\_s$.