= Ionic Coulomb coupling parameter
{title2=$\Gamma=Z^2e^2/(4\pi\epsilon_0a_i k_BT)$}
= Coulomb coupling parameter of ions
{c}
{synonym}
For one ionic species of <number density> $n_i$, the ion-sphere radius is $a_i=(3/(4\pi n_i))^{1/3}$. The ionic Coulomb coupling parameter compares the interaction energy from <Coulomb's law> at that separation with thermal energy $k_BT$. At fixed composition, $\Gamma\propto\rho^{1/3}/T$. Values near one mark significant corrections to the ideal ion gas; strong coupling can lead to an ordered solid. Screening, mixtures and quantum motion modify detailed transitions, so this estimate is not a universal crystallization boundary. It is separate from the electron degeneracy criterion based on the <electron Fermi temperature>.
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