Scattering Kinematics

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 .

The momentum and energy conservation impose that:

where 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)= ck . Considering that the energy losses or gains associated to phonon-like excitations are always much smaller than the energy of the incident photon (E <<E_i), 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.