Spin incoherence

Neutrons are sensitive not only to isotopic variation but to the breakdown of all spatial correlation. This includes the correlation of nuclear spins, through the neutron s own spin = 1/2. Without this extra incoherence, the scattering cross sections of chlorine would be 

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. 

The reduced mass enters quadratically into expressions for the atomic cross sections. 

It is easy to see that neutron diffraction experiments on hydrogenous materials are difficult because the coherent scattering is weak and the incoherent scattering is strong. Fortunately the heavier isotope. 

Neutron cross sections themselves follow no trend. Moreover, as was shown above, quite different values are foimd for different isotopes of the same element. This is extensively exploited in dif action studies of liquid solutions [4]. Occasionally, when isotopes of the same element have scattering lengths of opposite sign, the average coherent cross section can be reduced to zero by making a sample with the correct proportions of each isotope. Such null-scattering samples produce only incoherent signals. 

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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. 

In most cases, samples are a mixture of isotopes j with different scattering length bj and it is assumed that they are randomly distributed over the sample. Such random distribution of different isotopes produces incoherent cross-section. In analogy with isotope incoherence, spin incoherence is also observed. For nuclei with spin I l, the interaction depends on the orientation between neutron and nuclear spins scattering lengths and b for parallel and untiparallel spin, respectively, are different and the orientations of spins are randomly distributed in the nuclei even if they are the same kinds of nuclei. Then, incoherent and coherent atomic cross-sections are given by... 

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. 

The scattering length for an individual nucleus (i.e. the amplitude of the neutron wave which it scatters) is not the same for all nuclei of a particular element due to two factors. These are spin incoherence and isotopic incoherence. 

Spin incoherence is due to the fact that a neutron and a nucleus of spin I can form two different compound nuclei of spin the amplitude of the... 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

Both homonuclear and heteronuclear versions of relayed nOe experiments are known. The homonuclear relayed NOESY experiment involves both an incoherent transfer of magnetization between two spins H and H/ that are not coupled but close in space, and a coherent transfer of magnetization between two spins H(and H that are /-coupled together. The magnetization pathway may be depicted as... 

Oil and 0)2, and (b) 2D shift-correlation spectra, involving either coherent transfer of magnetization [e.g., COSY (Aue et al, 1976), hetero-COSY (Maudsley and Ernst, 1977), relayed COSY (Eich et al, 1982), TOCSY (Braunschweiler and Ernst, 1983), 2D multiple-quantum spectra (Braun-schweiler et al, 1983), etc.] or incoherent transfer of magnedzation (Kumar et al, 1980 Machura and Ernst, 1980 Bothner-By et al, 1984) [e.g., 2D crossrelaxation experiments, such as NOESY, ROESY, 2D chemical-exchange spectroscopy (EXSY) (Jeener et al, 1979 Meier and Ernst, 1979), and 2D spin-diffusion spectroscopy (Caravatti et al, 1985) ]. 

Fig. 2.9.7 Hahn spin-echo rf pulse sequence combined with bipolar magnetic field gradient pulses for hydrodynamic-dispersion mapping experiments. The lower left box indicates field-gradient pulses for the attenuation of spin coherences by incoherent displacements while phase shifts due to coherent displacements on the time scale of the experiment are compensated. The box on the right-hand side represents the usual gradient pulses for ordinary two-dimensional imaging. The latter is equivalent to the sequence shown in Figure 2.9.2(a).

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... 

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

Here, ojr is the rate of spinner rotation. I is the proton spin number, 8 is the chemical shift anisotropy (CSA) and q is the asymmetric parameter of the CSA tensor. Thus, the line broadening occurs when an incoherent fluctuation frequency is very close to the coherent amplitude of proton decoupling monotonously decreased values without such interference in Figure 1. 

In the theory of deuteron spin-lattice relaxation we apply a simple model to describe the relaxation of the magnetizations T and (A+E), for symmetry species of four coupled deuterons in CD4 free rotators. Expressions are derived for their direct relaxation rate via the intra and external quadrupole couplings. The jump motion between the equilibrium positions averages the relaxation rate within the same symmetry species. Spin conversion transitions couple the relaxation of T and (A+E). This mixing is included in the calculations by reapplying the simple model under somewhat different conditions. The results compare favorably with the experimental data for the zeolites HY, NaA and NaMordenite [6] and NaY presented here. Incoherent tunnelling is believed to dominate the relaxation process at lowest temperatures as soon as CD4 molecules become localized. 

Chemical shift correlated NMR experiments are the most valuable amongst the variety of high resolution NMR techniques designed to date. In the family of homonuclear techniques, four basic experiments are applied routinely to the structure elucidation of molecules of all sizes. The first two, COSY [1, 2] and TOCSY [3, 4], provide through bond connectivity information based on the coherent (J-couplings) transfer of polarization between spins. The other two, NOESY [5] and ROESY [6] reveal proximity of spins in space by making use of the incoherent polarization transfer (nuclear Overhauser effect, NOE). These two different polarization transfer mechanisms can be looked at as two complementary vehicles which allow us to move from one proton atom of a molecule to another proton atom this is the essence of a structure determination by the H NMR spectroscopy. 

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