Theories scattering function model calculation

Because there is no general microscopic theory of liquids, the analysis of inelastic neutron scattering experiments must proceed on the basis of model calculations. Recently1 we have derived a simple interpolation model for single particle motions in simple liquids. This derivation, which was based on the correlation function formalism, depends on dispersion relation and sum rule arguments and the assumption of simple exponential decay for the damping function. According to the model, the linear response in the displacement, yft), satisfies the equation... 

This article deals with one of the above mentioned subjects already treated in the 1940 s branched polymers. We present a survey of a number of scattering functions for special branched polymer structures. Hie basis of these model calculations is still the Flory-Stockmayer (FS) theory1,14,15) but now endowed with the more powerful technique of cascade theory which greatly simplifies the calculations. 

To what extent the schematic model systems A and B for a polymer melt show this typical relaxation behavior will be addressed in this subsection, by calculating various structural correlation functions that probe the dynamical changes of the melt on different length scales (Section 6.3.2.1). From these correlation functions it is possible to extract relaxation times the temperature dependence of which can be studied and compared to that of transport coefficients, such as the diffusion coefficient. This will be done in Section 6.3.2.2. The final paragraph of this subsection then deals with the calculation of the incoherent intermediate scattering function and its quantitative interpretation in the framework of the idealized mode coupling theory (MCT). " ... 

That final state scattering is of importance has been shown by Liebsch (53) and Liebsch and Plummer (54) who have performed calculations for a model system consisting of a localised s-type adsorbate orbital on a simple cubic substrate. The appropriate Bloch character of the final state wave function is taken into account within a multiple scattering theory such as has been applied in LEED calculations. 

The phase shifts <5, are calculated by standard partial-wave scattering theory. It involves the electron-atom interaction potential of the muffin-tin model. There are a variety of ways to obtain this potential, which consists of electrostatic and exchange parts (spin dependence may be included, especially when the spin polarization of the outgoing electrons is of interest). One usually starts from known atomic wave functions within one muffin-tin sphere and spherically averages contributions to the total charge density or potential from nearby... 

The focus then shifts to the delocalized side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field method (MS-SCF-ATa) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is... 

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