Inelastic coherent and incoherent

Inelastic coherent and incoherent scattering are proportional to the space and time Fourier transforms of, respectively, the pair-correlation and the selfcorrelation functions. Analogous to dynamic light scattering, these are used to probe polymer dynamics (Arbe et al., 2(X)3 Richter, 2003 Stepanek et al., 2002 Annis et al., 2001). 

With these parameters in hand, we then started to treat the on-resonance spectrum. It is very difficult to find a proper model to describe the mixture of elastic and inelastic (coherent and incoherent) scattering. The simplest approach, which ignores hyperfine interactions, was derived in Ref. 34. Here, we used a simple exponential decay to simulate the elastic scattering contribution. Then Eq. (12.10) becomes... 

Quasi-elastic Neutron Scattering. Coherent and incoherent inelastic neutron scattering are unique experimental techniques to characterize molecular motions on a time scale between 10 and 10 s. The continued development of high resolution inelastic scattering techniques in the past two decades (157-159) enables measurement of the dynamic structure factor S(Q, co) and the... 

Nuclear interactions between the neutron and the nucleus giving most of the elastic scattering and the inelastic scattering from the phonon contributions. The phonon contribution will consists of a number of terms the normal one-phonon, two-phonon (multiphonon) contribution from the coherent part of the cross section, and the density-of-states of the total phonon spectrum as seen by the incoherent cross section. Naturally, the ratio of these two contributions will depend on the relative coherent and incoherent cross sections. 

The terms elastic and inelastic scattering of electrons describe that which results in no loss of energy and some measureable loss of energy respectively. If the incident electron beam is coherent (i.e. the electrons are in phase) and of a fixed wavelength, then elastically scattered electrons remain coherent and inelastic electrons are usually incoherent. 

Direct geometry instruments also have advantages in this area. For many elements, the coherent cross section is larger than the incoherent cross section and with ( -resolved data it is possible to see additional structure [29,81] beyond that predicted by the scattering law, Eq. 2.32. These arise from coherent inelastic scattering and offer further possibilities for investigating the dynamics in such systems. 

In Ch. 21 Buntkowsky and Limbach review recent NMR work on the dynamics of dihydrogen and dideuterium in the coordination sphere of transition metals. In addition to inelastic neutron scattering and liquid state NMR, the effects of coherent (exchange couplings) and incoherent rotational tunneling of D2 pairs in transi-... 

Compton scattering is an inelastic X-ray scattering process where momentum is lost to the scattering electron. This means that the energy of the scattered X-ray is shifted to lower energy, and will not be involved in constructive or destructive interference with other scattered X-rays of the original energy. This means that Compton scattered X-rays are incoherent, and must be treated differently than other coherent and elastically scattered X-rays. 

Fundamentals. Neutrons can interact with matter in several ways. Depending on the neutron-nucleus interaction, they can be scattered coherently or incoherently and both processes can occur elastically or inelastically. For structural studies in electrochemical systems, diffraction, i.e. elastic coherent scattering, is of particular interest. Fundamentals of these modes of interaction, including spectroscopic aspects relevant for mobility studies, have been reviewed [989]. 

The solid states represent bounded atomic associations and the diffraction intensity is a result of coherently scattered wave interference. The neutron scattering can be coherent elastic or inelastic and incoherent. In coherent total scattering experiment both elastically and inelastically scattered neutrons are detected, thus performing energy integration over the whole range gives a value for The total differential cross-section is,... 

The theoretical model developed to explain these experiments is based on inelastic tunneling of electrons from the tip into the 2ir adsorbate resonance that induces vibrational excitation in a manner similar to that of the DIMET model (Figure 3.44(b)). Of course, in this case, the chemistry is induced by specific and variable energy hot electrons rather than a thermal distribution at Te. Another significant difference is that STM induced currents are low so that vibrational excitation rates are smaller than vibrational de-excitation rates via e-h pair damping. Therefore, coherent vibrational ladder climbing dominates over incoherent ladder climbing,... 

The time evolution in Eq. (7.75) is described by the time-dependent Schrodinger equation, provided the molecule is isolated from the rest of the universe. In practice, there are always perturbations from the environment, say due to inelastic collisions. The coherent sum in Eq. (7.75) will then relax to the incoherent sum of Eq. (7.74), that is, the off-diagonal interference terms will vanish and cn 2 — pn corresponding to the Boltzmann distribution. As mentioned earlier, the relaxation time depends on the pressure. In order to take advantage of coherent dynamics it is, of course, crucial that relaxation is avoided within the duration of the relevant chemical dynamics. 

Fig. 15. Basic equipment for measuring a nuclear inelastic scattering spectrum. Detector 1 measures the intensity of the incoherent nuclear forward scattering, which proceeds both elastically and inelas-tically detector 2 measures only the intensity of the coherent nuclear forward scattering, which proceeds elastically. Figure according to Ruffer and Chumakov (224).

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