  We present a detailed analysis of resonant inelastic scattering (RIXS) from
Fe$_{1.087}$Te with unprecedented energy resolution. In contrast to the sharp
peaks typically seen in insulating systems at the transition metal $L_3$ edge,
we observe spectra which show different characteristic features. For low energy
transfer, we experimentally observe theoretically predicted many-body effects
of resonant Raman scattering from a non-interacting gas of fermions.
Furthermore, we find that limitations to this many-body electron-only theory
are realized at high Raman shift, where an exponential lineshape reveals an
energy scale not present in these considerations. This regime, identified as
emission, requires considerations of lattice degrees of freedom to understand
the lineshape. We argue that both observations are intrinsic general features
of many-body physics of metals.
