= Number of electrons in a Debye sphere from a plasmon energy ratio
{c}
{title2=$N_D=8\sqrt2/(9\pi r^3)$}
For a three-dimensional ideal degenerate electron gas, let $r=\hbar\omega_{\rm pe}/E_F$. If one heuristically defines a <Debye length> by replacing $k_{\rm B}T$ with the <Fermi energy>, then $k_F\lambda_D=\sqrt2/r$ and the associated electron count is the displayed expression. A count below one signals failure of the classical many-particle screening interpretation. It does not prohibit plasmons. The zero-temperature compressibility instead gives the <Thomas-Fermi screening> length squared $2\epsilon_0E_F/(3n_ee^2)$.
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