Realistic Scattering Calculations

These results confirm and complement the earlier work of Beswick and Jortner who compared DWBA widths with those from collinear coupled-channel scattering calculations(33) where, as here, good agreement was observed. In the next section the DWBA widths are calculated for the chemically bonded HCO radical to give H+CO. Based on the present comparisons with exact results we are optimistic that the DWBA will provide realistic widths for this system. 

The first quantum reactive scattering calculations on a realistic four-atom reaction were done on the H2 + CN H + HCN reaction with linear geometry [10,11]. The first quantum reactive scattering calculation on a state-selected four-atom reaction with non-linear geometry was reported in 1991 [12] in which the reaction OH + H2 H2O + H and the reverse reaction H + H2O —> OH + H2 was... 

We show typical examples for the melt structure factor and for the single-chain structure factor in Figure 7. The upper panel is for a chemically realistic simulation of PB,111 where the scattering was calculated with the... 

A more realistic model for the secondary relaxation needs to consider motions of a molecular group (considered as a rigid object) between two levels. The group may contain N atoms with the scattering length h, at positions r (i=lj ). The associated motion may consist of a rotation aroimd an arbitrary axis, e.g. through the centre of mass depicted by a rotational matrix Q and a displacement by a translational vector . In order to evaluate the coherent dynamic structure factor, scattering amphtudes of the initial (1) and final (2) states have to be calculated ... 

Most models for SEF focus on the plasmonics, and treat the molecule as a classical dipole. While the plasmonics models increasingly give more realistic results for the plasmon observed in the system, the treatment of the molecule, and thus the molecule-metal system, is not always as well developed. In their 2005 paper, Johansson, Xu, and Kail [44] present a unified model of enhanced Raman scattering and enhanced fluorescence within the context of quantum optics. This model is easily modified to include the field enhancement (M) and decay enhancement (Md), which may be calculated through plasmonics methodology. 

Pseudostate calculations have the advantage over Born and optical-potential methods that they constitute a numerically-exact solution of a problem. The problem is not identical to a scattering problem but can be made quite realistic for useful classes of scattering phenomena by an appropriate basis choice. The state vectors, or equivalently the set of half-off-shell T -matrix elements, for such a calculation contain quite realistic information about the ionisation space. 

Theorists have been given enough detail to set up a calculation that can be expected to give a realistic description of an experiment. For scattering this level of detail is only given for methods that take into account the whole space of reaction channels, which is necessary in general to describe... 

The studies of Wiesenfeld [28] and Lai et al. [43] on the classical dynamics of a one-electron atom in a sinusoidal external field provide a physically realistic example in which the presence of KAM tori surrounding stable periodic orbits leads to deviations from the generic behaviour characteristic of a hyperbolic scattering system as discussed in Sect. 2. Although this system (10) seems simple, further studies illuminating the mathematical structures behind the scattering process, e.g. calculation of the Liapunov exponents of the unstable trapped orbits and the fractal dimension of the trapped set, have yet to be performed. 

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