Cross section incoherent

Recently it also became possible to observe directly the incoherent cross section of a protonated chain. As eluded to in Sect. 2.2, incoherent scattering... 

Figure 5.24 shows that this approach fails not only quantitatively but also qualitatively. Neither is the strong increase of the collective times relative to the self-motion in the peak region of Spair(Q) explained (this is the quantitative failure) nor is the low Q plateau of tpair(Q) predicted (this is the quaUtative shortcoming). We note that for systems hke polymers an intrinsic problem arises when comparing the experimentally accessible timescales for self- and collective motions the pair correlation function involves correlations between all the nuclei in the deuterated sample and the self-correlation function relates only to the self-motion of the protons. As the self-motion of carbons is experimentally inaccessible (their incoherent cross section is 0), the self counterpart of the collective motion can never be measured. For PIB we observe that the self-correlation function from the protonated sample decays much faster than the pair... 

Figure 9.17b schematically represents a cross-sectional view of the surface of a solid and represents the topmost layer of atoms by shaded circles. The open circles represent molecules in an ordered pattern on the solid substrate. Since the adsorbed molecules are ordered, their structure on the surface is characterized by what is called a supernet. Suppose we define <50 as the characteristic spacing of the substrate and 8S the equivalent quantity for the supernet. Then the two arrangements in Figure 9.17b are described by the ratios 5/60 = 4/1 and 8s/80 = 4/3. Building on the notion of reciprocal distances as developed in the discussion of Figure 9.15, it follows that the adsorbed layer with 8/80 = 4/1 should produce spots with a separation that is 1/4 that of the substrate. Likewise, for the case when 8s/80 = 4/3, a pattern of spots with a separation that is 3/4 that of the substrate is predicted. Thus, if the substrate produces spots at, say, 0 and 1, extra spots would be expected at 1/4, 2/4, and 3/4 for the 6/60 = 4 case, and at 3/4, 6/4, and 9/4 when 8s/80 = 4/3. The cases illustrated here are called coincident structures since the two patterns coincide periodically. When there is no correlation between two structures, they are said to be incoherent. 

Gs°(r, t) and Gsc(r, t) determine the incoherent differential scattering cross section for slow neutrons from CO through a weighted sum of their space-time Fourier transforms. Each of these functions is normalized to unity when integrated over all space. 

Incoherent inelastic neutron scattering is efficient in detecting M—H vibrations because the intensity of scattering is proportional to the square of the atomic vibrational amplitude (oc 1/atomic mass) and the scattering cross section (moderately high for H). HCo(CO)4 and H3M3(CO)12 (M = Mn and Re) have been studied, for example.93... 

S 1(q) characterizes the so-called incoherent scattering, while L 1(q) is related to the total cross section of all the inelastic scattering processes. With q —> 0, becomes the sum of squares of dipole matrix elements ... 

The first factor in square brackets represents the Thomson cross-section for scattering from a free electron. The second square bracket describes the atomic arrangement of electrons through the atomic form factor, F, and incoherent scatter function, S. Finally, the last square bracket contains the factor s(x), the molecular interference function that describes the modification to the atomic scattering cross-section induced by the spatial arrangement of atoms in their molecules. 

J H Hubbell, W J Veigele, E A Briggs, R T Brown, D T Cromer and R J Howerton (1975) Atomic form factors, incoherent scattering functions and photon scattering cross-sections. J. Phys. Chem. Ref. Data 4, 471 Errata in 1977, 6, 615. 

Figure 5 - Small angle neutron differential scattering cross section (ooo) measured from a sample consisting of sheets of PIP (N = 23000) and deuterated 1,2-PBD (N = 3200) which were in contact for 162 hours at 52°C. The scattering contrast significantly exceeds the incoherent background (—) determined from measurements on the individual polymers, evidencing the thermodynamic miscibility of the blend.

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