Scattering single

One of the major advantages of SEXAFS over other surface structutal techniques is that, provided that single scattering applies (see below), one can go direcdy from the experimental spectrum, via Fourier transformation, to a value for bond length. The Fourier transform gives a real space distribudon with peaks in at dis-... 

Rgure 3 Experimental and calculated results (a) for epitaxial Cu on Ni (001). The solid lines represent experimental data at the Cu coverage indicated and the dashed lines represent single-scattering cluster calculations assuming a plane wave final state for the Cu IMM Auger electron A schematic representation lb) of the Ni (010) plane with 1-5 monolayers of Cu on top. The arrows indicate directions in which forward scattering events should produce diffraction peaks in (a). 

Collimated Single Scattered beam crystal radiation... 

We will consider the theoretical description of EXAFS based on the single-scattering short-range order formalism. The EXAFS can... 

A relative crystallinity or "crystallinity index" has been used as an approximate method [55,56]. The simplest procedure involves determination of the intensity at a single scattering angle (26), in reference to the value for the amorphous halo at the same angular reflection. This method, for example, was useful to follow the variation of crystallinity of an iPP during isothermal melting [57]. 

Path Parameters Generated by FEFF (Single Scattering) for Cementite... 

In this way, the geometry-dependent Casimir fluctuations can be extracted from the m//W/ /e-scattcri ng part of the scattering matrix. The determinant of the n-spherc/disk S-matrix can be separated into a product of the determinants of the 1-sphere/disk S-matrices S E, a,i), where a, are the radii of the single scatterers, and the ratio of the determinant of the multi-scattering matrix M(k) and its complex conjugate (A. Wirzba., 1999) ... 

Here the energy E and the wave number k are related as E = h2k2/ 2rn. When inserted into Krein s formula, the product over the single-scatterer determinants generates just the bulk (or Weyl term) contribution to the density of states... 

The superposition principle allows us to assume just a single scatterer in the view of the radar. The transmitted signal hits this scatterer whose distance (we measure distance and time in the same units) from the (collocated) transmitter and receiver is r. Assume that the scatterer is stationary. The return signal will be a delayed version of the original, delayed by the total round trip time from the radar to the scatterer. Specifically the signal voltage at the antenna of the receiver is... 

For particles of heavy atoms such as Au or Pt it is not sufficient to assume that the calculations of diffraction patterns can be made by use of the simple, single-scattering, kinematical approximation. This leads to results which are wrong to a qualitatively obvious extent (16). The calculations must be made using the full dynamical diffraction theory with the periodic... 

Within this approximation, at least half of the photons that contribute to reflectance of a semi-infinite layer have been scattered only once. On (5-irradiation this part of photons is reflected from the illuminated surface with an exponential time profile Jo(t) = 2 xNoSac-exp(-(Sa + K )c-t), where N, is the number of incident photons at t = 0. Considering a weakly absorbing and not too strongly scattering sample (A = 1 cm S 102 cm-1), the decay time of the single-scattered photons is in the order of r = 500 fsec. The second half of photons is multiply scattered and decays... 

For the purpose of solving crystal stmctures, this leaves us with the problem of ensuring that one has single-scattering conditions. The failure of this condition has been the subject of hundreds of papers - a good analysis... 

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