= Degenerate-plasma Langmuir dispersion
{title2=$\omega^2=\omega_p^2+\tfrac35k^2v_F^2+O(k^4)$}
The long-<wavelength> root of the <degenerate-plasma dielectric response>. Expanding its <logarithm> at large $s=\omega/(kv_F)$ gives $\epsilon=1-\omega_p^2/\omega^2-3\omega_p^2k^2v_F^2/(5\omega^4)+\cdots$. The occupied <Fermi sphere> has $\langle v_\parallel^2\rangle=v_F^2/5$, accounting for the dispersive coefficient. The static electron response instead defines the <Thomas-Fermi screening length> $v_F/(\sqrt3\omega_p)$.
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