Wigner–Seitz radius
The Wigner–Seitz radius formula_1, 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, formula_1 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, formula_1 is calculated for bulk materials. Formula. In a 3-D system with formula_4  free electrons in a volume formula_5, the Wigner–Seitz radius is defined by where formula_7 is the particle density of free electrons. Solving for formula_1 we obtain The radius can also be calculated as where formula_11 is molar mass, formula_12 is amount of free electrons per atom, formula_13 is mass density, and formula_14 is the Avogadro number. This parameter is normally reported in atomic units, i.e., in units of the Bohr radius. Values of formula_1 for the first group metals: