Nuclear spin incoherence

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. 

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 ... 

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... 

In principle all the rotational transitions of dihydrogen are observable by INS spectroscopy but some transitions are rather weak since the incoherent neutron scattering cross section used generally in this book is inapplicable ( 2.1). This derives from the strict nuclear spin correlation found in dihydrogen, Transitions within the separate para- or orthohydrogen manifolds are controlled by the coherent cross section of hydrogen, 1.76 bam, and these transitions are too weak to be observed in its INS spectmm. 

This last expression, (6.3), has been derived for fixed nuclei but the separation process into incoherent and coherent terms carries over into all kinds of neutron scattering theory. Moreover, it is particularly important for hydrogen. Remembering that the number of quantum states associated with a compound nuclear spin of J will be 27 -I- 1, we find that the average scattering length taken over the two spin states of hydrogen can be written ... 

Quite often, spin dephasing times are orders of magnitude shorter than the decay times measured in the (incoherent) population relaxation experiments. For a few transition metal chelates in the excited triplet state we will argue later that the homogeneous spin dephasing is determined by hyperfine interactions of the triplet electron spin with randomly flipping ligand nuclear spins. 

Because the temperature of a realistic nuclear spin system is not at zero degrees absolute, the internal interaction Hamiltonians always contain two parts one is stationary or coherent, the other fluctuating or incoherent, or random. The former part usually determines the positions of the peaks in a spectrum, the latter part governs the dynamics of the system. However, they may become entangled under certain conditions. For spin-1/2 systems, r.f. interactions can be made larger than the internal interactions in most cases, thus the manipulation of the interactions with r.f. pulses is realizable. This is an advantage of NMR over many other spectroscopies. In fact, most experimental methods in NMR spectroscopy correspond to certain manipulations of the internal interactions. For quadrupolar spin systems, the internal... 

Incoherent elastic neutron scattering exists only for nuclei with spin (i.e. not for zero-spin nuclei such as or 0), and results from the interaction of random nuclear spin orientations with the spin of the incident neutrons. It is spatially isotropic. It is usually negligible, except again in the case of nuclei where it becomes very large. This is most useful since it constitutes the basis of neutron scattering curve normalization on an absolute scale through the use of a HjO reference sample (Section 2.5). 

In many materials the scattering nuclei have a random distribution of nuclear spin orientations and/or a random distribution of isotopic constitution. If the scattering length varies with spin state or isotope, this will lead to a separation of the scattering into a coherent and an incoherent portion. The coherent portion will contain interference between the waves from the various scattering nuclei, but the incoherent portion will be obtained from the sum of the squares of the various scattering amplitudes rather than from the square of the sum. 

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... 

Figure 4- SE signal as a function of the phase difference between the incident and scattered beams. The upper part of the figure shows the principle difference, in the case of deuterons and protons, between the scattering from a nucleus with and without nuclear spin. The lower part shows the NSE signals obtained in both cases—the count rate is plotted against the current of the phase correction coil. Acob und vdincoh ore the echo amplitudes for coherent and incoherent scattering, No is the average count rate outside the echo, N+ and iV are the maximal and minimal count rates with the ir/2-flippers on, and Nap and iVdown are the count rates of spin-up (rr-flipper off) and spin-down (ir-flipper on) measurements made with the nl2-flippers off.

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. 

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. 

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 ...

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-... 

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