The inelastic scattering process is depicted schematically in Figure 1.


Schematics of the inelastic scattering process. The incident and scattered photons are characterised by their energy E, wave vector k and polarisation vector epsilon.

The momentum and energy conservation impose that:


where theta is the scattering angle between the incident and scattered photons. The relation between momentum and energy in the case of photons is given by: E(k)= H1ck . Considering that the energy losses or gains associated to phonon-like excitations are always much smaller than the energy of the incident photon (E <<Ei), one obtains:


The ratio between the exchanged momentum and the incident photon momentum is completely determined by the scattering angle. Therefore, for IXS, there are no limitation in the energy transfer at a given momentum transfer for phonon-like excitations, in strong contrast to INS where a strong coupling between energy- and momentum transfer exists.