Shadow scattering

The intensity of SS /. from an element in the solid angle AD is proportional to the initial beam intensity 7q, the concentration of the scattering element N., the neutralization probability P-, the differential scattering cross section da(0)/dD, the shadowing coefficient. (a, 5j ) and the blocking coefficient(a,5 ) for the th component on the surface ... 

B1.23.2.3 SCATTERING AND RECOILING ANISOTROPY CAUSED BY SHADOWING AND BLOCKING CONES... 

A) TIME OF FLIGHT SCATTERING AND RECOILING SPECTROMETRY (TOF-SARS)—SHADOW CONE BASED EXPERIMENT... 

Figure Bl.23.9. Scattering intensity of 4 keV Ne versus azimuthal angle 8 for a Ni 110] surface in the clean (1 X 1), (1 X 2)-H missing row, and (2 x l)-0 missing row phases. The hydrogen atoms are not shown. The oxygen atoms are shown as small open circles. 0-Ni and Ni-Ni denote the directions along which O and Ni atoms, respectively, shadow the Ni scattering centre.

This relation is a direct consequence of the conservation of flux. The target casts a shadow in the forward direction where the intensity of the incident beam becomes reduced by just that amount which appears in the scattered wave. This decrease in intensity or shadow results from interference between the incident wave and the scattered wave in the forward direction. Figure B2.2.2 for the density P (r) of section B2.2.6 illustrates... 

An important concept is the shadow cone, which is a region where no ions can penetrate due to the ion—nucleus repulsion (see Figure 2). This effect makes ion scattering surface sensitive. The size of the shadow cone / jCan be calculated for the classical Coulomb potential as ... 

In scattering Intensity Is treated here. It would be wrong to Imply that other factors, such as shadowing and the target atom s electron configuration, do not play a role. Clearly, they do, but their effects do not alter our conclusions. Thus, It appears that LEISS may also be quite valuable as a qualitative probe for changes In surface morphology.(16)... 

The kitchen has an ancient bottled-gas stove, a Formica table with an oil lamp on it and a scatter of jewelry tools and materials, a tiled fireplace laid ready with raw-smelling coal, and a beautiful inlaid Queen Anne wall clock tocking away in the corner, showing the phases of the moon and the movement of the sun through the zodiac. As I head out of the back door and find the privy, a black shadow of a cat with blue eyes slips past my legs and away like warm smoke. 

Fig. 1.3 Relaxation map of polyisoprene results from dielectric spectroscopy (inverse of maximum loss frequency/w// symbols), rheological shift factors (solid line) [7], and neutron scattering pair correlation ((r(Q=1.44 A )) empty square) [8] and self correlation ((t(Q=0.88 A" )) empty circle) [9],methyl group rotation (empty triangle) [10]. The shadowed area indicates the time scales corresponding to the so-called fast dynamics [11]...

Fig. 4.15 Momentum transfer (Q)-dependence of the characteristic time r(Q) of the a-relaxation obtained from the slow decay of the incoherent intermediate scattering function of the main chain protons in PI (O) (MD-simulations). The solid lines through the points show the Q-dependencies of z(Q) indicated. The estimated error bars are shown for two Q-values. The Q-dependence of the value of the non-Gaussian parameter at r(Q) is also included (filled triangle) as well as the static structure factor S(Q) on the linear scale in arbitrary units. The horizontal shadowed area marks the range of the characteristic times t mr- The values of the structural relaxation time and are indicated by the dashed-dotted and dotted lines, respectively (see the text for the definitions of the timescales). The temperature is 363 K in all cases. (Reprinted with permission from [105]. Copyright 2002 The American Physical Society)...

Therefore, Cext is a well-defined observable quantity we measure U with and without the particle interposed between source and detector. Because Cext is inherently positive, the effect of the particle is to reduce the detector area by Cext this, then, is the interpretation of Cext as an area. In the language of geometrical optics we would say that the particle casts a shadow of area Cext However, as stated previously, this shadow can be considerably greater—or much less—than the particle s geometrical shadow. We note from (3.33) that Cext is the maximum observable extinction. The scattering term fi(D) X =0/k2 cannot be greater than Csca and is positive therefore, the observed extinction Cext lies within the limits... 

It is at once obvious that Fourier transformation of equation (2.2) should yield information about all the j shells in direct space that contribute to the EXAFS. The Rjs so obtained are, however, shortened by the k-dependent part of /k). Since the intensity of the outgoing spherical wave decreases very rapidly with increasing R, distant atoms contribute very little to the fine structure. Multiple scattering effects are also relatively unimportant and these have indeed been ignored in the derivation of equation (2.2). EXAFS should contain no information about shadowed or eclipsed atoms, but there are exceptions to this. Other theoretical approaches also use similar effects to explain the EXAFS. 

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