Dynamic scattering, description

Electron dynamic scattering must be considered for the interpretation of experimental diffraction intensities because of the strong electron interaction with matter for a crystal of more than 10 nm thick. For a perfect crystal with a relatively small unit cell, the Bloch wave method is the preferred way to calculate dynamic electron diffraction intensities and exit-wave functions because of its flexibility and accuracy. The multi-slice method or other similar methods are best in case of diffraction from crystals containing defects. A recent description of the multislice method can be found in [8]. 

The molecular beam and laser teclmiques described in this section, especially in combination with theoretical treatments using accurate PESs and a quantum mechanical description of the collisional event, have revealed considerable detail about the dynamics of chemical reactions. Several aspects of reactive scattering are currently drawing special attention. The measurement of vector correlations, for example as described in section B2.3.3.5. continue to be of particular interest, especially the interplay between the product angular distribution and rotational polarization. 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

The preferable theoretical tools for the description of dynamical processes in systems of a few atoms are certainly quantum mechanical calculations. There is a large arsenal of powerful, well established methods for quantum mechanical computations of processes such as photoexcitation, photodissociation, inelastic scattering and reactive collisions for systems having, in the present state-of-the-art, up to three or four atoms, typically. " Both time-dependent and time-independent numerically exact algorithms are available for many of the processes, so in cases where potential surfaces of good accuracy are available, excellent quantitative agreement with experiment is generally obtained. In addition to the full quantum-mechanical methods, sophisticated semiclassical approximations have been developed that for many cases are essentially of near-quantitative accuracy and certainly at a level sufficient for the interpretation of most experiments.These methods also are com-... 

Figure 3 Calculated X-ray diffuse scattering patterns from (a) a full molecular dynamics trajectory of orthorhombic hen egg white lysozyme and (b) a trajectory obtained by fitting to the full trajectory rigid-body side chains and segments of the backbone. A full description is given in Ref. 13.

The bond fluctuation model not only provides a good description of the diffusion of polymer chains as a whole, but also the internal dynamics of chains on length scales in between the coil size and the length of effective bonds. This is seen from an analysis of the normalized intermediate coherent scattering function S(q,t)/S(q,0) of single chains ... 

As will be shown in Section 3, inelastic X-ray scattering experiments can help to decide which theoretical approach is appropriate. One must keep in mind that this static correction is far from an appropriate description of electron correlations. A more accurate way is to account for dynamical screening by writing %(q, co) in terms of the one-particle Greens function G(p, e) corrected for many-particle effects by a... 

The detailed microscopic description of a chemical reaction in terms of the motion of the individual atoms taking part in the event is known as the reaction dynamics. The study of reaction dynamics at surfaces is progressing rapidly these years, to a large extent because more and more results from detailed molecular beam scattering experiments are becoming available. 

Analysis of polyelectrolytes in the semi-dilute regime is even more complicated as a result of inter-molecular interactions. It has been established, via dynamic light-scattering and time-dependent electric birefringence measurements, that the behavior of polyelectrolytes is qualitatively different in dilute and semi-dilute regimes. The qualitative behavior of osmotic pressure has been described by a power-law relationship, but no theory approaching quantitative description is available. 

One of the most striking features of the scattered spectrum for either neutrons or light in the vicinity of a phase transition is the appearance of a divergent elastic or quasielastic peak centred near zero frequency shift that lies entirely outside the quasiharmonic soft-mode description of the dynamics (Fleury Lyons, 1983). The first observation of a divergence in scattered intensity is due to Yakovlev et ai, (1956), who observed the phenomenon in the a-fi transition of quartz. The scattered intensity increases dramatically, sometimes by a factor of 10000 near and the maximum value of line width of the diverging feature is itself rather small ( 1 cm ). In Fig. 4.7, typical central peaks are shown for the purpose of illustration. 

This section introduces the principal experimental methods used to study the dynamics of bond making/breaking at surfaces. The aim is to measure atomic/molecular adsorption, dissociation, scattering or desorption probabilities with as much experimental resolution as possible. For example, the most detailed description of dissociation of a diatomic molecule at a surface would involve measurements of the dependence of the dissociation probability (sticking coefficient) S on various experimentally controllable variables, e.g., S 0 , v, J, M, Ts). In a similar manner, detailed measurements of the associative desorption flux Df may yield Df (Ef, 6f, v, 7, M, Ts) where Ef is the produced molecular translational energy, 6f is the angle of desorption from the surface and v, J and M are the quantum numbers for the associatively desorbed molecule. Since dissociative adsorption and... 

In this chapter we summarize the current status of the low-energy scattering of noble-gas metastable atoms in molecular beams. A brief summary of potential scattering theory that is relevant to the understanding of collision dynamics, as well as a description of the experimental method, precedes the presentation of experimental findings. The experimental results presented are mainly from the authors laboratories. 

After these general results and remarks concerning quantum dynamics, we turn now to the more detailed description of the scattering of particles, including reactive scattering. 

Equation (4.162) displays clearly how the cross-section is determined from the scattering dynamics in the radial coordinate via the time evolution of the initial state and a subsequent projection onto the final state. The angular momentum L = /l(l + l)K lh is according to Eq. (4.30) in the classical description related to the impact parameter, i.e., L = fivob. Thus, the sum can be interpreted as the contribution of all impact parameters. In the classical description only one impact parameter contributed to the differential cross-section. For a hard-sphere potential, it can be shown that da/dQ = d at low energies, which is four times the classical result in Eq. (4.44). 

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