Interpretation of the polarizability

[daudaudaudau]

Hello!

If one uses the Lindhard formula to calculate the static polarizability of an electron gas, $\chi(q)$, you get a function which is pretty much a constant until $q=2k_F$ with $k_F$ being the Fermi wave vector. After this it decays(it's on page 335 of Ashcroft and Mermin). But what is the interpretation of this? Somehow short wavelengths are not screened very well?

 

[daudaudaudau]

bump :)=

 

[DrDu]

For k<2k_K, you can understand static screening in therms of Thomas-Fermi theory, i.e. the external potential modifies the local Fermi Energy and the filling of the orbitals, in terms of perturbation theory, you work with zeroth order wavefunctions and change only occupation, due to the degeneracy of the electron gas, this costs little energy. For higher values of k >2k_F, you really have to bend the electronic wavefunctions which costs more energy (I would guess of the order of min(k-2k_F)*k_F/m=min(k-2k_F)*v_F).