Scattering localized atomic

A representative example of this localized atomic scattering is that of the photolysis of HCl adsorbed on LiF(OOl), studied by Rydberg-atom TOF spectroscopy, which is described in (Section 23.4). The adsorption geometry of HCl on LiF(OOl) is well known from FTIR studies, which show that HCl molecules in the first ad-layer are hydrogen bonded to the surface, with a tilt angle of 19 5° from the surface plane. Once prepared, the HCl adsorbate is photolysed by p-polarized 193.3 nm radiation from an excimer laser. The H atoms formed in the HCl photodissociation are further excited via a two-step process to a high-n... 

Figure 27.16 Localized atomic scattering of H from HCl on LiF(OOl). Photolysis by 193.3 nm photons results in an elastic scattering angle of 40°. The drawing is to scale, using van der Waals radii for chlorine (ra = 1.75 A), calculated from the internuclear distances in solid hydrogen halides at 80 K. Reproduced from Giorgi et al, 3. Chem. Phys., 1999, 110 598, with permission of the American Institute of Physics...

In Chapter 27 we studied the photochemistry of the adsorbate state, and we discussed the occurrence of localized atomic scattering as a key feature characterizing the photofragmentation dynamics of adsorbed molecules. Furthermore, it was shown how the concept of localized atomic scattering extended to that of localized atomic reaction, in which the new bond created at the surface takes place in an adjacent location to the old (broken) bond. 

The atomic PDF is related to the probability to find a spherical shell around a generic atom (scattering center) in the material - it is defined as G(r) = Anp[p r)-p(, where p r) and po are, respectively, the local and average atomic number densities and r the radial distance. G(r) is the Fourier transform of the total structure factor Sid). ... 

Keywords Local atomic structure Neutron scattering Pair-density function ... 

In a true scattering problem, an incident wave is specified, and scattered wave components of ifr are varied. In MST or KKR theory, the fixed term x in the full Lippmann-Schwinger equation, f = x + / GqVms required to vanish, x is a solution of the Helmholtz equation. In each local atomic cell r of a space-filling cellular model, any variation of i// in the orbital Hilbert space induces an infinitesimal variation of the KR functional of the form 8 A = fr Govi/s) + he. This... 

There are two ways for including the contribution from bulk water. One was first introduced in fiber diffraction analysis of polynucleotides. It subtracts the X-ray scattering contribution of bulk water from the individual atomic scattering factors used in the structure analysis [700,836], The other incorporates the continuous electron density of liquid water, 0.34 e/A3, in the electron density calculations. As a result the more localized solvent atoms are I more clearly defined in difference electron density maps [837]. 

UPS from Adsorbate Core Levels.—As outlined above, an out-going photoelectron in its final state is a super-position of two coherent contributions a direct wave whose amplitude and symmetry are determined by the intra-atomic transition at the emitting site and an indirect wave generated by repeated scattering of the direct wave by the local atomic environment. It was suggested by Liebsch that this final-state scattering should lead to angular variations in the photoemission spectrum and would be examined best in core-level emission, which involves the simplest possible initial... 

Here the authors consider the possibility of inferring such statistical characteristics from the spectral features of probe photons or particles that are scattered by the density fluctuations of trapped atoms, notably in optical lattices, in two hitherto unexplored scenarios, (a) The probe is weakly (perturbatively) scattered by the local atomic density corresponding to the random occupancy of different lattice sites, (b) The probe is multiply scattered by an arbitrary (possibly unknown a priori) multi-atom distribution in the lattice. The highlight of the analysis, which is based on this random matrix approach, is the prediction of a semicircular spectral lineshape of the probe scattering in the large-fluctuation limit of trapped atomic ensembles. Thus far, the only known case of quasi-semicircular lineshapes in optical scattering has been predicted [Akulin 1993] and experimentally verified [Ngo 1994] in dielectric microspheres with randomly distributed internal scatterers. 

Solvent causes a net softening of the local atomic potentials, particularly for exposed sidechain atoms, with a commensurate increase in fluctuation amplitudes. Recent inelastic neutron scattering studies of lysozyme as a function of hydration are in accord with this conclusion.2551 In addition, there are significant localized conformational changes, particularly for sidechains and exposed loop regions, and these, coupled with the increased fluctuations observed in the solvent simulation, may be of functional importance. These points are amplified in Chapt. X, where a thermodynamic analysis of the effect of solvent on the conformational equilibria of a dipeptide model is given. 

Interest in determination of higher order correlation functions of local atomic distribution in complex systems has stimulated the growth of XANES. In fact XANES is sensitive via multiple scattering, to the geometrical arrangement of the environment surrounding the absorbing atom. 

In most materials, however, the modification of the forces at the surface is such that the surface localized modes have frequencies which lie below the frequencies of an associated bulk band with the same symmetry they have the appearance of having been peeled down from this bulk band [24]. In the usual case, the lowest energy of all these peeled -down modes derives from the bulk transverse acoustic band and is normally sagittally polarized. This dispersion branch is called the Rayleigh wave (RW) because it was predicted by Lord Rayleigh from continuum wave theory over a century ago [38]. Helium atom scattering experiments on virtually every material so far investigated have detected the RW on clean crystalline surfaces. 

The ionic insulators discussed in some detail in the previous section have closed shell electronic configurations similar to the noble gases and electronic distributions which are localized around the electronic core. The principal interactions are Coulombic, although their polarizabilities appear to influence greatly the response of the electronic distribution to surface lattice vibrations. For other materials, particularly metals and some layered compounds, the conduction and valence electrons are best thought of as somewhat delocalized if not entirely free. These electrons are what the helium atoms scatter from, and their states of motion are significantly modulated by the vibrations of the atomic cores. Thus, for these materials HAS is very... 

A qualitatively new approach to the extended fine structure in the secondary electron spectrum was proposed in [33-35]. Bearing in mind the autoionization mechanism, the authors suggested allowing for the coherent elastic scattering of electrons of both intermediate state of autoionization and the final state, i.e., the electrons detected in an experiment. In the context of this approach, the secondary electron extended fine structure results from superposition of two interference terms, both of which are determined by the local atomic environment of the ionized atom. One of them is determined by the wave number of the intermediate-state electron of autoionization, and the other by the wave number of the final-state electron detected in the experiment. 

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