Scattering elastic/inelastic

SANS Small-angle neutron scattering [175, 176] Thermal or cold neutrons are scattered elastically or inelastically Incident-Beam Spectroscopy Surface vibrational states, pore size distribution suspension structure... 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

Neutrons may collide with nuclei causing one of the following reactions inelastic scattering, elastic scattering, radiative capture, or fission. 

One way to think about the Landauer formula is to say conductance is scattering [69]. In fact, conductance is elastic scattering, because in the original Landauer approach, all scattering is considered to be elastic - particles leave the electrode and are scattered elastically until they make it into the other electrode (or not). Inelastic events are not included, at least conceptually. 

FIG. 1.2 Feynman diagrams describing (a) elastic scattering, (b) inelastic scattering. Source Feil (1975). 

Figure 2.4 Different types of interactions of electrons with a solid 1, X-ray or optical photons 2, back-scattered electrons 3, secondary electrons 4, coherent elastic scattering 5, inelastic scattering 6, incoherent elastic scattering.

The interpretation given above is simplified, since fluorescence is not the only process that allows the atom to lose its excess energy. Other phenomena such as Rayleigh scattering (elastic scattering) and the Compton effect (inelastic scattering with release of Compton electrons) can complicate the X-ray emission spectrum. 

The electrons that are not scattered elastically lose their energy on penetrating a phosphor crystal by inelastic scattering and formation of secondary electrons. 

The energy analysis of these inelastically scattered electrons is carried out by a cylindrical sector identical to the monochromator. The electrons are finally detected by a channeltron electron multiplier and the signal is amplified, counted and recorded outside of the vacuum chamber. A typical specularly reflected beam has an intensity of 10 to 10 electrons per second in the elastic channel and a full width at half maximum between 7 and 10 meV (60-80 cm l 1 meV = 8.065 cm-- -). Scattering into inelastic channels is between 10 and 1000 electrons per second. In our case the spectrometer is rotatable so that possible angular effects can also be studied. This becomes important for the study of vibrational excitation by short range "impact" scattering (8, 9, 10). 

The relations discussed above can be generalized to elastic, inelastic, and reactive scattering of two molecules for any initial conditions. A detailed discussion of these results is presented in Appendix C. 

The fluorescence technique, like other methods based on scatter (elastic or inelastic), has been shown by us - and others to be a reliable unperturbing method of measuring spatial/ temporal flame temperatures and species concentrations. To avoid the dependency of the fluorescence signal on the environment of the emitting species, it has been shown by several workers that optical saturation of the fluorescence process (i.e., the condition occurring when the photoinduced rates of absorption and emission dominate over the spontaneous emission and colli sional quenching rates) is necessary. Pulsed dye lasers have sufficient spectral irradiances to saturate many transitions. Our work has so far been concerned with atomic transitions of probes (such as In, Pb, or T1) asoirated into combustion flames and plasmas. 

As previously mentioned, the evanescent wave could interact with the optically rare medium not only by being absorbed but also by being scattered either elastically (Rayleigh Scattering) or inelastically (Raman Scattering). Because it is not within the scope of this paper to review the complete history and theory of Raman scattering, further information is indicated in Ref. 

It is not strictly correct to equate the inelastic mean free path with the attenuation length, as we do so essentially in Fig. 1. One would have to assume in the experiment that as many electrons are scattered elastically into as out of the direction of the analyser slits. Because of the net loss due to back scattering this can never be the case in practice. 

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