Friedel oscillation wavelength from carrier density ($\lambda =\pi /(3{\pi }^{2}n{)}^{1/3}$)

A single isotropic three-dimensional valley with two equal spin populations has $n=k_F^3/(3{\pi }^2)$. A density oscillation at wavevector $2k_F$ therefore has the wavelength in the title. This depends on carrier density, independently of effective mass and dielectric screening strength. Extra valley degeneracy, spin polarization or reduced dimensionality changes the state-counting relation.