We present an approximation for efficient calculation of the Lindhard susceptibility $chi^{L}(q,omega)$ in a periodic system through the use of simple products of real space functions and the fast Fourier transform (FFT). The method is illustrated by
providing $chi^{L}(q,omega)$ results for the electron doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_{4}$ extended over several Brillouin zones. These results are relevant for interpreting inelastic X-ray scattering spectra from cuprates.
We have carried out first-principles calculations of the Compton scattering spectra to demonstrate that the filling of the hole Fermi surface in LaO$_{1-x}$F$_{x}$FeAs produces a distinct signature in the Fourier transformed Compton spectrum when the
momentum transfer vector lies along the [100] direction. We thus show how the critical concentration $x_c$, where hole Fermi surface pieces are filled up and the superconductivity mediated by antiferromagnetic spin fluctuations is expected to be suppressed, can be obtained in a bulk-sensitive manner.
