Behavior of the electron-gas dielectric function nearq=2kF

Whether or not the exchange and correlation correction $G\left(q\right)\mathrm{}$ to the dielectric function of an electron gas has a sharp peak at $q=2\mathrm{}{k}_F$ is a longstanding and unresolved problem. Using pseudopotential theory and a model dielectric function that has a peak in its $G\left(q\right)\mathrm{}$, we have calculated the effects of such a peak on the lattice dynamics of potassium. It is found that the phonon frequencies in a certain region of reciprocal space are altered in a unique way (by the peak) and that this effect can be resolved by neutron scattering experiments. We suggest that the question of whether or not there is a prominent peak in $G\left(q\right)\mathrm{}$ can be settled by carrying out inelastic-neutron scattering experiments on potassium to measure phonon-dispersion curves along a [$0.280.14\xi$] trajectory in reciprocal space.