  We study resonant inelastic x-ray scattering (RIXS) peaks corresponding to
low energy particle-hole excited states of metallic FeTe and semi-metallic
TiSe$_2$ for photon incident energy tuned near the $L_{3}$ absorption edge of
Fe and Ti respectively. We show that the cross section amplitudes are well
described within a renormalization group theory where the effect of the core
electrons is captured by effective dielectric functions expressed in terms of
the the atomic scattering parameters $f_1$ of Fe and Ti. This method can be
used to extract the dynamical structure factor from experimental RIXS spectra
in metallic systems.
