Coherent scattering cross-section

If the displacements of the atoms are given in terms of the harmonic normal modes of vibration for the crystal, the coherent one-phonon inelastic neutron scattering cross section can be analytically expressed in terms of the eigenvectors and eigenvalues of the hannonic analysis, as described in Ref. 1. 

The key requirements for ISRS excitation are the existence of Raman active phonons in the crystal, and the pulse duration shorter than the phonon period loq1 [19]. The resulting nuclear oscillation follows a sine function of time (i.e., minimum amplitude at t=0), as shown in Fig. 2.2e. ISRS occurs both under nonresonant and resonant excitations. As the Raman scattering cross section is enhanced under resonant excitation, so is the amplitude of the ISRS-generated coherent phonons. 

Table 3.1. Neutron coherent scattering cross-sections b and neutron absorption coefficients fi/o (A = 1.08 A) for elements found in biological molecules. [183]...

Table 3.4. Coherent scattering cross-sections b (10"13 cm) scattering by atomic groups occurring in biological macromolecules, based on Table 3.1...

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)... 

Figure 30. Zimm plot of the absolute coherent scattering cross-section reduced to the concentration of deuterated species for sample B in the directions z ( ) and x ( ) compared to an isotropic sample (full line). The curves extrapolated at zero q are found to intersect at the same value. From their initial slope, one can calculate Rg and Rg x.

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). 

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