= Electron-acoustic recoil length
{title2=$\lambda=\hbar/(2m_ec_s)$}
For free-electron recoil and a linear acoustic branch, $E_e(q)=\hbar^2q^2/(2m_e)$ and $E_{\rm ph}(q)=\hbar c_sq$. Their ratio is $q\lambda$, so equality occurs at $q=1/\lambda$. This is a momentum/localization crossover scale, formally half a sound-speed analogue of the <Reduced Compton wavelength>. It does not replace the speed of light in electron relativity or determine a <mean free path>. A Fermi-surface electron emitting a phonon has fractional radial loss $\delta\simeq q/(2\lambda k_F^2)$ when the transferred energy is small.
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