Nuclear incoherent scattering

From (3.39) we see that nuclear coherent scattering is always non spin-flip (-(- -(-,--), as is nuclear incoherent scattering which is due to the random iso-... 

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 ... 

Fig. tt.5-2tta,b BaTiOs. Triple-axis neutron spectrometer scans at constant frequency across the sheet of diffuse scattering at 150 °C. The path of the scans is shown in the inset, (a) shows the elastic scan (v = 0), where the high background level is due to nuclear incoherent scattering, (b) Ineleastic scan (v = 0.97 x 10 Hz)... 

Fig. 41. Response of YbPdjSij as measured with 5 = 12.5meV. This illustrates how the quasielastic response at higher temperatures changes to an inelastic response (top panel) at T=5 K. The hatched areas are due to both nuclear incoherent scattering and to phonons. The area that is not hatched between the fiill and dashed lines represents the scattering from the impurity phase. (From Weber et al. 1989b.)...

Fig. 15. Basic equipment for measuring a nuclear inelastic scattering spectrum. Detector 1 measures the intensity of the incoherent nuclear forward scattering, which proceeds both elastically and inelas-tically detector 2 measures only the intensity of the coherent nuclear forward scattering, which proceeds elastically. Figure according to Ruffer and Chumakov (224).

Table 2 Bound scattering lengths, i>(fm) and cross section for selected isotopes and for selected naturally occurring isotopic mixtures of the elements u(hams, 1 bam = 100 fm ). Z, atomic number A, mass number I, spin of the nuclear groimd state i>coh> bine, coherent and incoherent scattering lengths ffa, ffeCh, coherent and incoherent cross sections ffa, absorption cross section for 2.2 km s neutrons ...

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). 

The first two terms are the nuclear coherent (3.15) and incoherent scattering (3.9) and the last term is the purely magnetic scattering (3.26). The third term is an interference term between nuclear and magnetic scattering and is zero if ij x, if the scattering is purely nuclear or purely magnetic, and if P = 0. P describes the polarization of the incident beam (0 < P < 1). 

G is corrected by the subtraction of a constant p to exclude a 8(q) term from S(q,u>). To establish the relationship in Eq. (2.75) the nuclear scattering lengths have to be expressed in terms of the coherent and the incoherent scattering lengths. For this purpose the following equation can be used... 

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