Multiple scattering representation

Most recently, Freed (84) has developed a generalized theory in terms of a multiple scattering representation of scattering of fluid waves by the polymer molecules and derived the precise result ... 

K. F. Freed and A. Perieo. Consideration on the multiple scattering representation of the concentration dependence of the viscoelastic properties of polymer systems. Macromolecules, 14 (1981), 1290-1298. 

Figure 2. Schematic representation of two models for the origin of electron energy-loss nearedge structures (ELNES) for the core-ionization edges, (a) Transition of strongly bound core electrons into unoccupied states (b) multiple scattering description of ELNES.

Fig 3, Representation of copper-imidazole coordination showing the important multiple-scattering pathways. 

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). 

The solntion of the system of equations (6) can be obtained by iteration. This representation of the solution corresponds to the expansion of the coefficients multiple-scattering series. The first two terms of this... 

The outline of the present chapter is as follows. Section 2 deals with the relevant physical, electronic, and magnetic properties of the lanthanides. Section 3 reviews briefly the above-mentioned theoretical methods, with the focus on the SIC-LSDA method, and, in particular, the full implementation of SIC, involving repeated transformations between Bloch and Wannier representations (Temmerman et al., 1998). This is then compared with the local-SIC, implemented in the multiple scattering theory (Liiders et al., 2005). Section 4 deals with the valence (Strange et al., 1999) and valence transitions of the lanthanides. Section 5 discusses the local magnetic moments of the lanthanides. Section 6 discusses two spectroscopies applied to lanthanides and some of their compoimds. Section 7 outlines a methodology of calculating the finite temperature (T) properties of the lanthanides and their... 

Implementations have been realized using Gaussian functions (GTO s) ([38, 39] and Slater-type orbitals (STO s) [5, 40, 41], and numerical basis sets [42, 43, 44]. The auxiliary basis may be avoided by the use of a purely numerical representation of the potential on a grid (usually called DVM - Discrete Variational Method [45, 5]), by certain approximations for the potential (Multiple Scattering concept within the so-called mufl5n-tin approximation - [46]), the linear combination of muffin-tin orbitals [47, 3], and in connection with the pseudopotential concept the application of plane-wave basis expansions - see, e.g.. Ref. [112]. 

Strom [189], The various terms obtained by a formal expansion of the inverse in (2.82) can be interpreted as various multiple-scattering contributions to the total transition matrix. Indeed, using the representation... 

Since the decomposition of D + into the representations of the point-symmetry group contains the totally symmetric one, the cross section G (3w, Aw) is nonzero for any molecule. The selection rules for G2(3w, Aw) coincide with the ones for the symmetric contribution to the Rayleigh scattering discussed earlier. In particular, for symmetrical-top molecules, independent of the multiplicity of their states, the contribution G (3w, Aw) is nonzero. Therefore the degeneracy in such molecules does not result in any peculiarities in the depolarization of the scattering in the third harmonic. 

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