Polar coordinates scattering calculation

Let us consider the scheme showed in Fig. I to calculate the field scattered by a rough cylindrical surface (i.e. a wire). The wire is illuminated by a monochromatic, linearly polarized plane wave at an angle of incidence a with its axis of symmetry. The surface is described, in a system fixed to the wire, by p = h (cylindrical coordinates. We shall denote the incident wave vector lying on the x-z plane as kj and the emergent wave vector simply as k. 

The analysis of the polarised neutron experiment on K2NaCrFe (Fig. 9) has been completed< >. The aspherical form factor component/4(0 was shown to be particularly sensitive to the covalent spin distribution, and the shape of fi Q) supported the inference for eg spin polarization drawn from the comparison of powder neutron diffraction data and resonance data (Section VI. B). A preliminary report of the form factor determination for both tetra-hedrally and octahedrally coordinated Fe + in YaFesOis by polarized neutrons has been given ). The form factors are not the same and that for tetrahedral Fe + is contracted relative to that for octahedral Fe +, which follows closely the calculated free-ion curve. The ligand forward peak (Section VI. B) has been directly observed ) in a measurement of the critical scattering of neutrons by ferromagnetic K2CUF4. 

We have presented the hyperspherical coordinate formulation for e + T elastic and inelastic scattering using local surface functions and have shown that it is both efficient and accurate. It can in principle be extended to energies above the ionization threshold by including hyperspherical harmonics in the surface function basis set. It also permits a calculation of polarization cross sections. This approach is very promising and should lead to a very complete description of the e H scattering processes. 

For single crystal samples, the crystal-fixed coordinate system is identical to the laboratory system. Therefore the intensities of the Raman scattered light in the various polarization components can be obtained directly in terms of the polarizability component derivatives from Table II of Brith, Ron, and Schnepp (1969) (reproduced from Wilson, Decius and Cross, 1955), If, however, a randomly oriented powder is investigated, the results must be averaged over orientations, a procedure also described in these two references. If the derivatives have been calculated with respect to the symmetry coordinates S, the derivatives with respect to the normal eoordinates are given in analogy to (4.10). Finally, the observed intensity is obtained by substitution in the equation as follows (Woodward, 1967) ... 

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