Ideal scattering experiment

In an ideal scattering experiment the collisions are assumed to occur at a fixed point in space. In practice the collision volume is finite and the part viewed by the detecting system generally depends on the scattering angle. Care must therefore be taken in relating the scattered particle intensity to the cross section. 

The most detailed information on the collision process can be obtained from laser spectroscopy of crossed-beam experiments, where the initial quantum states of the collision partners before the collision are marked, and the scattering angle as well as the internal energy of the reactants is measured. In such an ideal scattering experiment aU relevant parameters are known (Sect. 8.5). 

Figure B2.3.1. Schematic diagram of an idealized molecular beam scattering experiment.

The overall result is that in the melt the polymer molecules adopt Gaussian configurations and behave as thermodynamically ideal entities. This combination of ideality and chain entanglement has been confirmed by neutron scattering experiments and is well established despite the apparent paradox. 

It is always easy to calculate idealized scattering curves for perfect networks. The experimental systems vary from the ideal to a greater or lesser degree. Accordingly, any estimate of the correctness of a theoretical analysis which is based on an interpretation of experiment must be put forth with caution since defects in the network may play a role in the physical properties being measured. This caveat applies to the SANS measurement of chain dimensions as well as to the more common determinations of stress-strain and swelling behavior. 

Contrary to the previous case, parvalbumin binds only two Ca ions. Compared to the technical difficulties encountered at the K-absorption edge of calcium due to increased absorption of 3 A wavelengths, the quantitative replacement of Ca by terbium ions (Lj-edge at 1.648 A) offers an ideal way to obtain structural information about the ion binding sites of parvalbumin by resonance scattering experiments. In fact, Miake-Lye, Doniach and Hodgson were able to determine for the first time the distance between the center of mass of the parvalbumin and its two terbium ion binding sites in solution. 

MgO is a particularly well studied oxide the structure of the (100) single crystal surface is extremely flat, clean, and stoichiometric. Recent grazing incident X-ray scattering experiments have shown that both relaxation, -0.56 0.4%, and rumpling, 1.07 0.5%, are extremely small [66]. However, no real crystal surface consists of only idealized terraces. A great effort has been undertaken in recent years to better characterize the MgO surface, in particular for polycrystalline or thin-film forms which in some cases exhibit an heterogeneous surface, due to the presence of various sites. All these sites can be considered as defects. The identification and classification of the defects is of fundamental importance. In fact, the presence of appreciable concentrations of defects can change completely the chemical behavior of the surface. A typical example is that of the reaction of CO on MgO (see 3.1). 

Fluid microstructure may be characterized in terms of molecular distribution functions. The local number of molecules of type a at a distance between r and r-l-dr from a molecule of type P is Pa T 9afi(r)dr where Pa/j(r) is the spatial pair correlation function. In principle, flr (r) may be determined experimentally by scattering experiments however, results to date are limited to either pure fluids of small molecules or binary mixtures of monatomic species, and no mixture studies have been conducted near a CP. The molecular distribution functions may also be obtained, for molecules interacting by idealized potentials, from molecular simulations and from integral equation theories. 

Studies of similar structural transitions for hydrogen within the nanotubes have been carried out by Xia et al. [145], Ying et al. [146], and Ma et al. [147] These results exhibit a wide variety of linear, cylindrical, and helical phases, the existence of which is strongly dependent on the tube radius and the molecular density. Obviously, the transitions between these novel phases are of considerable interest, but space considerations prevent us from discussing the results in detail. Scattering experiments would provide ideal probes of these phases but their interpretation wiU be difficult unless the tubes are aligned. 

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