The Wigner–Seitz radius 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. This parameter is used frequently in condensed matter physics to describe the density of a system.
In a 3-D system with N particles in a volume V , the Wigner–Seitz radius is defined by
4 3 π r s 3 = V N . Solving for r s we obtain
r s = ( 3 4 π n ) 1 / 3 , where n is the particle density of the valence electrons.
For a non-interacting system, the average separation between two particles will be 2 r s . The radius can also be calculated as
r s = ( 3 M 4 π ρ N A ) 1 3 , where M is molar mass, ρ is mass density, and N A is the Avogadro number.
This parameter is normally reported in atomic units, i.e., in units of the Bohr radius.
Values of r s for single valence metals are listed below:
