Electron scattering theory

This text covers quantitative analysis by electron energy-loss spectroscopy in the electron microscope along with instrumentation and applicable electron-scattering theory. 

Although the electron scattering theory, basic principles of experimentation and interpretation are the same at any temperature, high-temperature conditions pose specific problems in the experiments and interpretation of the data . ... 

L. S. Bartell, The status of electron scattering theory with respect to accuracy in structure analyses, in I. Hargittai and M. Hargittai (eds), Stereochemical applications of gas-phase electron diffraction, VCH Publishers, Weinheim, (1988). 

An analogous quantity, the generalized oscillator strength, is found to be useful in electron-scattering theory. It is a function of the momentum K transferred from the incident electron to the molecule and has the form5... 

The conclusions to be drawn from series of measurements of this type, illuminating some new aspects of electron scattering theory, are interesting a- 100 but completely beyond the scope of the present chapter. 

Equation (8.3) provides a common basis for the major computational methods used in low-energy electron scattering theory. The terms containing Q(H — E)Q 1 in this equation describe polarization response and other correlation effects in terms of a matrix optical potential. Singularities due to this energy denominator cancel out exactly [264, 265, 270],... 

This surprising effect has no explanation within conventional theories of elementary chemical reactions and / or neutron (and electron) scattering theory. It is attributed to very short, attosecond entanglement of a scattering proton with adjacent particles, which can be studied by NCS (and ECS) due to the very short scattering time (i.e., the characteristic time window) of these experimental methods. To date there exist various theoretical models describing this new effect [Karlsson 2000 Karlsson 2002 (c) Karlsson 2003 (a) Chatzidimitriou-Dreismann 2003 (b) Chatzidimitriou-Dreismann 2004 (a)]. 

Weinberger, P. (1990) Electron Scattering Theory for Ordered and Disordered Matter. Oxford University Press. 

J. Jensen, A. R. Mackintosh Rare earth magnetism 80. R. Gastm lns, T. T. Wu The ubiquitous photon 79. P. Luchini, H. Motz Undulators and free-electron lasers 78. P. Weinberger Electron scattering theory... 

High harmonic generation (HHG) is the production of many harmonics (sometimes hundreds) of the input frequency from medium intensity lasers. Here TDDFT calculations have been successful for some atoms " ° and molecules. " " Several experiments have used the HHG response of molecules to determine their vibrational modes, " and calculations have been performed using traditional scattering theory. " " If HHG response develops into a new spectroscopy, the electron scattering theory discussed above may be of utility to treat large molecules. 

B1.6.2.1 BETHE-BORN THEORY FOR HIGH-ENERGY ELECTRON SCATTERING... 

A type of molecular resonance scattering can also occur from the formation of short-lived negative ions due to electron capture by molecules on surfrices. While this is frequently observed for molecules in the gas phase, it is not so important for chemisorbed molecules on metal surfaces because of extremely rapid quenching (electron transfer to the substrate) of the negative ion. Observations have been made for this scattering mechanism in several chemisorbed systems and in phys-isorbed layers, with the effects usually observed as smaU deviations of the cross section for inelastic scattering from that predicted from dipole scattering theory. 

It should be noted that a comprehensive ELNES study is possible only by comparing experimentally observed structures with those calculated [2.210-2.212]. This is an extra field of investigation and different procedures based on molecular orbital approaches [2.214—2.216], multiple-scattering theory [2.217, 2.218], or band structure calculations [2.219, 2.220] can be used to compute the densities of electronic states in the valence and conduction bands. 

All ab initio applications of multiple scattering theory in dilute substitutional alloys rely on the one-to-one correspondence configuration. This holds both for the calculation of transition probabilities [7], represented by Eq. (7), and the electronic structure [8], represented by the Green s function equation [9]... 

In this section we will discuss perturbation methods suitable for high-energy electron diffraction. For simplicity, in this section we will be concerned with only periodic structures and a transmission diffraction geometry. In the context of electron diffraction theory, the perturbation method has been extensively used and developed. Applications have been made to take into account the effects of weak beams [44, 45] inelastic scattering [46] higher-order Laue zone diffraction [47] crystal structure determination [48] and crystal structure factors refinement [38, 49]. A formal mathematical expression for the first order partial derivatives of the scattering matrix has been derived by Speer et al. [50], and a formal second order perturbation theory has been developed by Peng [22,34],... 

Figure 9. The measured momentum density of an aluminium film. In the left panel we show the measured momentum density near the Fermi level (error bars), the result of the LMTO calculations (dashed line) and the result of these calculations in combination with Monte Carlo simulations taking into account the effects of multiple scattering (full line). In the central panel we show in a similar way the energy spectrum near zero momentum. In the right panel we again show the energy spectrum, but now the theory is that of an electron gas, taking approximately into account the effects of electron-electron correlation (dashed) and this electron gas theory plus Monte Carlo simulations (solid line).

Kirtley J, Soven P (1979) Multiple-scattering theory of intensities in inelastic-electron-tunneling spectroscopy. Phys Rev B 19 1812-1817... 

As in scattering theory in general, one can treat the role of V in either a time independent or a time dependent point of view. The latter is simpler if the perturbation V is either explicitly time dependent or can be approximated as such, say by replacing the approach motion during the collision by a classical path. Algebraic methods have been particularly useful in that context,2 where an important aspect is the description of a realistic level structure for H0. Figure 8.3 is a very recent application to electron-molecule scattering. 

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