Resonance scattering models

Transmission Coefficients from Analytically Solvable Resonance Scattering Models... 

The analysis of the theoretical results is consistent with the resonant scattering model. The nondispersive (localized) rattling guest vibrations intersect the acoustic branches of the lattice modes. The avoided-crossings provide the... 

Initial femtochemistry theoretical models were simply generalizations of those for the single-photon DIET processes, i.e., as dynamics induced by multiple electronic transitions (DIMET) [100]. The idea is simply that even if the excited state residence is too short to cause excitation to a ground state continuum after resonant scattering (tR < tc), it can still cause some vibrational excitation in the ground state. If resonant... 

Very often it is not possible to obtain all basic scattering functions with the same accuracy. Even worse, in resonant scattering we are often left with the cross term I ,(h) only. This is still quite an acceptable situation, if the resolution to a monopole approximation of the structure is required, as A fh) and B fh) may be determined completely from the two remaining functions I (h) and I (h). However a straight-forward method for the evaluation of higher multipoles in the sense of the above calculation then does not exist any more. The analysis of resonant scattering in this case has to refer to models. 

The first experiments on resonant scattering of counterion distributions fall into the early period of the operation of the EMBL instrument XI5. Among the studies on polyacrylic acid, desoxyribonucleic acid (DNA) and ribosomes in various solvents, those on Cs-DNA gave the clearest answer with respect to the counter ion distribution. Another advantage was that the results could be compared with the existing double helic model with its predictable counter ion distribution. ... 

Since the parallel components of the dynamic dipole are active in RAIRS, it is possible to use the azimuthal dependence to obtain the orientation of the adsorbate at the surface. A similar technique has been applied to adsorbates on metals in HREELS measurements made off specular in order to observe parallel modes through impact or resonant scattering processes. This was first demonstrated for the Rh(CO)2 molecule on anisotropic TiO2(110) surface [72]. The results of this study also allow a test of the three layer model theory (Fig.5,6) as applied to S-polarised radiation. Fig. 11 shows the FT-RAIRS spectrum for 1/3 monolayer of Rh(CO)2 on Ti02(l 10) measured with P and S polarised radiation. 

The Mie scattering model also helps explain the strong polarization anisotropy or antenna effects [9, 12] in the Raman scattering of semiconductor NWs, so named because of the selective Raman scattering of TM-polarized light by way of this structural resonance modulation. This behavior is quantifled in the polarization anisotropy ratio, calculated by an averaging of the squared held amplitudes of the product of incident and scattered flelds [12], determined from a Mie-type solution ... 

Fig. 12 Boron Ka and resonance scattering spectra of milled h-BN(a) and cluster model used for DV-Xa calculations(b)...

The large branching ratios predicted by the multiple scattering model is certainly an Indication of the poor representation of the R dependence of the molecular ion potential in this model. It is important to note that substantial non-Franck-Condon behavior of this branching ratio occurs at photon energies well above the peak position of the resonance (27). 

To this group belong several models of very different kinds such as the image model (RE-IE), the charge transfer (RE-CT) model, the electron-hole excitation model (RE-EH), and the Raman reflectivity model (RE-RF). These models have very little in common except that they all lead to enhancements by virtue of a resonance scattering mechanism. The validity of the last statement is not always realized by people, but it will be shown below to hold true. 

Natoli CR (1983) Near-edge absorption stracture in the framework of the multiple scattering model. Potential resonance on barrier effects. In A Bianconi, L Incoccia, S Stipcich (eds) EXAFS and Nearedge Stracture. Springer Ser Chem Phys 27 43-47... 

A. U. Hazi and H. S. Taylor, Stabilization method of calculating resonance energies—model problem, Phys. Rev. A, A7 1109 (1970). H. S. Taylor and J. K. Williams, Proposed theory of calculating the energy of negative-ion resonant elastic scattering states of electronic spectroscopy, J. Chem. Phys. 42 4603 (1965). 

To follow the scale of complexity, the review is divided into three parts. The first two parts deal with the key concept of effective Hamiltonians which describe the dynamical and spectroscopic properties of interfering resonances (Section 2) and resonant scattering (Section 3). The third part. Section 4, is devoted to the resolution of the Liouville equation and to the introduction of the concept of effective Liouvillian which generalizes the concept of effective Hamiltonian. The link between the theory of quantum resonances and statistical physics and thermodynamics is thus established. Throughout this work we have tried to keep a balance between the theory and the examples based on simple solvable models. 

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