Incoherent scattering cross-section

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... 

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.

Figure 1. Relative coherent and incoherent scattering cross-sections for some zeolite atomic species.

Table 1 Coherent Scattering Lengths, Incoherent Scattering Cross Sections, and Absorption Cross Sections for Some Elements...

Element Coherent scattering length (cm X 10 ) Incoherent scattering cross section (cm x 10 ) Absorption cross section (cm X 1024)... 

The aqueous LiCl solution with the composition of LiC1.6.0H2O was prepared in the same way as described for the X-ray samples. In the aqueous solution the proton ( H) has a very large incoherent scattering cross section the observed differential scattering cross section can be approximated to the incoherent dynamic structure factor through... 

If b+ and b- are of different sign [e.g., H, V) there is a small coherent cross section and a large incoherent cross section. For this reason vanadium is used as a ccilibrant in incoherent scattering cross-section measurements (see below) and as a sample container (for polycrystaUine materials) for many of the experiments described below so that unwanted peaks are not introduced into the diffraction pattern. On the other hand, if an element has one isotope of zero nuclear spin in large abundance the scattering is almost entirely coherent [e.g., 0, Fe). 

For nuclear incoherent scattering from a non-magnetic system with randomly oriented nuclear spins, the cross-sections per atom are independent of the neutron polarization direction and the spin-flip scattering cross section is twice that for non spin-flip scattering ... 

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