Inelastic scattering efficiency

It is theoretically possible to predict F and for different probes, but it is difficult to achieve generality because the results depend on sample properties such as transparency and inelastic scattering efficiency. Nevertheless, for a given type of sample, such as a clear, deep liquid, Fs or F can provide a direct prediction of relative signal strength. 

The X-ray spectrum observed in PIXE depends on the occurrence of several processes in the specimen. An ion is slowed by small inelastic scatterings with the electrons of the material, and it s energy is continuously reduced as a frmction of depth (see also the articles on RBS and ERS, where this part of the process is identical). The probability of ionizii an atomic shell of an element at a given depth of the material is proportional to the product of the cross section for subshell ionization by the ion at the reduced energy, the fluorescence yield, and the concentration of the element at the depth. The probability for X-ray emission from the ionized subshell is given by the fluorescence yield. The escape of X rays from the specimen and their detection by the spectrometer are controlled by the photoelectric absorption processes in the material and the energy-dependent efficiency of the spectrometer. 

The total contribution to the Auger electron signal is then dependent upon the attenuation length (kM) in the matrix before being inelastically scattered, and upon the transmission efficiency of the electron spectrometer as well as the efficiency of the electron detector. Calculated intensities of Auger peaks rarely give an accuracy better than 50%, and it is more reliable to adopt an approach which utilises standards, preferably obtained in the same instrument. 

There is some experimental evidence to indicate that much of the enhancement is associated with surface roughness (local microstructures) in the range of 1 to 100 nm. At resonance with th microparticle modes the local electric field at the incident frequency (h L) becomes large near and on the particle surface. Furthermore, the re-radiation efficiency of Raman active molecules situated near the surface also becomes enhanced when the inelastically scattered frequency (hco,) is also in resonance with these microparticle modes. The Raman scattering intensity of the adsorbed molecule is then given by... 

In addition, the spatial distribution of the inelastically scattered electrons carries a strong forward-bias such that the majority of the signal can be collected by the on-axis post-specimen EELS spectrometer commonly employed in the AEM. This makes EELS a far more efficient technique in terms of signal collection than XEDS, where the detector samples only a tiny fraction (< 1%) of the emitted X-ray photons. An energy resolution of less than 1 eV in the EELS spectrum is readily achievable in most commonly available instrumentation a value that is far superior to the 150 eV spectral resolution of XEDS. Finally, and perhaps most uniquely, with careful analysis, the EELS spectrum can also yield information related to the electronic structure and inter-atomic bonding present in the specimen, both of which are not detectable with the XEDS technique. 

We have presented the hyperspherical coordinate formulation for e + T elastic and inelastic scattering using local surface functions and have shown that it is both efficient and accurate. It can in principle be extended to energies above the ionization threshold by including hyperspherical harmonics in the surface function basis set. It also permits a calculation of polarization cross sections. This approach is very promising and should lead to a very complete description of the e H scattering processes. 

Reactive scattering, in which the products of a collision are chemically different from the reactants, is formally similar to inelastic scattering. However, there are complications that arise from the fact that a basis set that efficiently describes the reactants is usually inefficient to describe the products and vice versa. Even the coordinate system to be used requires some care for example, Jacobi coordinates... 

The main problem with the Raman spectrometers is the weakness of the Raman scattering. Only one in 10 incident photons is inelastically scattered. Powerful lasers (argon, krypton or helium—neon) are used. The laser beam has to be focused accurately on the specimen surface. The scattered light is recorded at 90° to the incident light beam. The discrimination of Raman scattering from Rayleigh scattering is accomplished by the use of a very efficient monochromator system, photomultiplier and amplifier. 

In their original paper Miller and Jansen op de Haar only applied their method to simple elastic and inelastic scattering tests [16]. The first practical demonstration of its efficiency came, when Zhang and Miller used the method to calculate J=0 reaction probabilities, over quite a wide energy range, for the already heavily studied H-I-H2 reaction [102]. Their results agreed well with the earlier calculations, and appeared to be quite easy to converge. 

Molecular projectiles offer the possibility of additional direct inelastic channels, namely, the excitation or de-excitation of the molecular internal modes, much as for gas-phase molecular inelastic scattering. Unlike a gas-phase collision of a molecule with a structureless projectile, here the energy balance of the internal modes of the molecule need not be met entirely by the translation. The participation of the surface degrees of freedom is possible and the low-energy modes of the surface, not only phonons but also electron-hole pairs, are particularly important in bridging the gap (remember the exponential gap principle) and thereby making such inelastic collisions quite efficient. 

Typically, a high-pressure (0.1-1.0 torr) buffer gas is used to thermalize the electrons (emitted from a heated filament) by inelastic scattering and positive ion ionization processes. Ideally, the buffer gas should not form stable anions, and buffer gases that have been used include He, H2, N2, CH4, NH3, CO2 and i-C4HjQ. Polyatomic gases such as CH4, NH3 i-C4HJQ or CO2 have proven to be most efficient in promoting electron capture. The first three have seen the most use, in part because they are often used in Bronsted acid Cl and are readily available. 

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