Section 4.3.4.1.2. Parameters involved in the description of a single inelastic scattering event

The importance of inelastic scattering as a function of energy and momentum transfer is governed by a double differential cross section: where d corresponds to the solid angle of acceptance of the detector and d(ΔE) to the energy window transmitted by the spectrometer. The experimental conditions must therefore be defined before any interpretation of the data is possible. Integrations of the cross section over the relevant angular and energy-loss domains correspond to partial or total cross sections, depending on the feature measured. For instance, the total inelastic cross section corresponds to the probability of suffering any energy loss while being scattered into all solid angles. The discrimination between elastic and inelastic signal is generally defined by the energy resolution of the spectrometer, that is the minimum energy loss that can be unambiguously distinguished from the zero-loss peak; it is therefore very dependent on the instrumentation used.

The kinematics of a single inelastic event can be described as shown in Fig. 4.3.4.2 . In contrast to the elastic case, there is no simple relation between the scattering angle and the transfer of momentum . One has also to take into account the energy loss ΔE. Combining both equations of conservation of momentum and energy, and one obtains where the fundamental units = Bohr radius and = Rydberg energy are used to introduce dimensionless quantities. In this kinematical description, one deals only with factors concerning the primary or the scattered particle, without considering specifically the information on the ejected electron. For a core-electron excitation of an atom, one distinguishes q (the momentum exchanged by the incident particle) and χ (the momentum gained by the excited electron), the difference being absorbed by the recoil of the target nucleus (Maslen & Rossouw, 1983).

Figure 4.3.4.2| top | pdf | A primary electron of energy E0 and wavevector k is inelastically scattered into a state of energy E0 − ΔE and wavevector k′. The energy loss is ΔE and the momentum change is ħq. The scattering angle is θ and the scattered electron is collected within an aperture of solid angle dΩ.