Degenerate-plasma zero-point sound ($\omega =\pm k{v}_F(1+\delta ),\delta \sim 2e^{-2-2k^2{v}_F^2/(3{\omega }_p^2)}$)

The short-wavelength root of the degenerate-plasma dielectric response, approaching the edge of the occupied parallel velocity interval from outside. Writing $s=1+\delta$ makes its logarithmic singularity give the exponentially small positive correction in the title. It is the high-wavenumber limit of the charged Langmuir wave branch in this approximation; neutral zero sound has a different interaction and long-wavelength limit.