# Wigner_Seitz_radius¶

plasmapy.formulary.quantum.Wigner_Seitz_radius(n: Unit(‘1 / m3’))

Calculate the Wigner-Seitz radius, which approximates the inter-particle spacing.

This function returns the radius of a sphere whose volume is equal to the mean volume per atom in a solid. This parameter is often used to calculate the coupling parameter. When ion density is used, this is the ion sphere radius, i.e., the space occupied by a single ion with no other ions in that space. Higher density means less space for each ion, so the radius is smaller.

Parameters

n (Quantity) – Particle number density.

Returns

radius – The Wigner-Seitz radius in meters.

Return type

Quantity

Raises
Warns

UnitsWarning – If units are not provided, SI units are assumed.

Notes

The Wigner-Seitz radius approximates the interparticle spacing. It is the radius of a sphere whose volume is equal to the mean volume per atom in a solid:

$r = \left(\frac{3}{4 π n}\right)^{1/3}$

Example

>>> from astropy import units as u
>>> Wigner_Seitz_radius(1e29 * u.m**-3)
<Quantity 1.33650462e-10 m>