Spin-incoherent scattering

The spin-incoherent scattering (prominent for protons) involves a change of the spin-state of the scattered neutrons (spin-flip scattering) with a probability of%. 

See also, Bacon, G.E. "Thermal Neutron Diffraction", 3rd ed. Oxford University Press Oxford, 1976, for a discussion of spin-incoherent scattering as well as other aspects of the theory and practice of neutron scattering. 

Coherent and isotopic-incoherent scattering involve no spin-flip, whereas spin incoherent scattering (i.e., for hydrogenated molecules) inverts the neutron spin with a probability of 2/3. Since spin-polarized neutrons are used in the neutron spin-echo technique, the polarization of the neutron beam, after spin-incoherent scattering woifld be reversed and three times less intense. 

The consequences of spin-incoherent scattering, which can have a significantly deleterious effect on the NSE signal, are shown in Figure 4. Spin-incoherent scattering causes, with a nucleus-dependent probability, a spin flip of both the inelastically and elastically scattered neutrons, e.g., 2/3 of the neutrons scattered from H undergo a spin flip, whereas deuterium, which has no nuclear spin, has no influence on the neutron spin. 

Measurements of the self-correlation function with neutrons are normally performed on protonated materials since incoherent scattering is particularly strong there. This is a consequence of the spin-dependent scattering lengths of hydrogen. Due to spin-flip scattering, which leads to a loss of polarization, this... 

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). 

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 ... 

The amplitude of the neutron wave scattered by a nucleus of a given element varies from one isotope to another and also between the two spin states of the neutron-nucleus system. In addition to coherent scattering (leading to diffraction effects) this variation of scattered amplitude from atom to atom of the same species produces incoherent scattering in which there is no systematic interference between scattered... 

However, because of the nuclear spin incoherence of " Cl, the total incoherent cross section of chlorine is oinc (Cl) = 5.30 bam. Spin incoherence is particularly important for an understanding of the neutron scattering cross section of hydrogen nuclei. In = 1/2. 

This potential is spin-dependent. When the radiation is scattered by a set of elementary centres, this dependence is the origin of the so-called coherent and incoherent scattering. The potential thus defined produces an isotropic collision around the incidence axis. 

Simple neutron scattering by an assembly of nuclei with non-zero spin coherent and incoherent scattering... 

Given that the spin-up and spin-down neutron scattering lengths of a proton are 1.080 x 10-12 cm, and —4.737 x 10 12 cm, respectively, verify that the incoherent scattering cross section amc is indeed as high as 79.7 bams. 

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