Wigner–Seitz radius

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The Wigner–Seitz radius , 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.[1] This parameter is used frequently in condensed matter physics to describe the density of a system.


In a 3-D system with particles in a volume , the Wigner–Seitz radius is defined by[1]

Solving for we obtain

where is the particle density of the valence electrons.

For a non-interacting system, the average separation between two particles will be . The radius can also be calculated as

where is molar mass, is mass density, and is the Avogadro number.

This parameter is normally reported in atomic units, i.e., in units of the Bohr radius.

Values of for single valence metals[2] are listed below:

Li 3.25
Na 3.93
K 4.86
Rb 5.20
Cs 5.62

See also[edit]


  1. ^ a b Girifalco, Louis A. (2003). Statistical mechanics of solids. Oxford: Oxford University Press. p. 125. ISBN 978-0-19-516717-7. 
  2. ^ *Ashcroft, Neil W.; Mermin, N. David (1976). Solid State Physics. Holt, Rinehart and Winston. ISBN 0-03-083993-9.