“…29 IXS relies on the energy and momentum transfers measured from a high-energy incident photon in the X-ray range that is defined by its wave vector, energy, and polarisation ( k 1 , ħω 1 , ε 1 ) by the electron system and the scattered photon ( k 2 , ħω 2 , ε 2 ) defined by the same parameters. 30,31 The measured energy transfer ħω is given by the law of conservation of energy, ħω = ħω 1 − ħω 2 and momentum transfer q is a function of the scattering angle. The number of photons being measured in a certain energy range is defined by the double differential scattering cross-section (DDSCS),
where according to Fermi's Golden rule and under first-order perturbation theory, the probability of the transition from a ground state to a final state can be described; on one hand, it is related to Thomson scattering, associated with the strength of photon–electron coupling and, on the other hand, it is related to the strength of the DSF S ( q , ω ), which is directly related to the allowed excitations of the scattering system.…”