Total spin coherence

Formally, multi-quantum coherences of order p are described by irreducible tensor operators Tqp (cf. Table 3.1.2 for coupled spins [Eml]. The coherence order is described by p = mf-mi (cf. Fig. 2.2.11), where m and /n, are the final and initial magnetic quantum numbers of a transition. For double-quantum coherence, for example, p = 2. The total spin coherence q corresponds to the maximum order possible. In this case, p = q so that maximum coherence order is described by T,. 

The spin state of a paramagnetic system with total spin S wiU lift its (25 + l)-fold degeneracy under the influence of ligand fields (zero-field interaction) and applied fields (Zeeman interaction). The magnetic hyperfine field sensed by the iron nuclei is different for the 25 + 1 spin states in magnitude and direction. Therefore, the absorption pattern of a particular iron nucleus for the incoming synchrotron radiation and consequently, the coherently scattered forward radiation depends on how the electronic states are occupied at a certain temperature. 

Such a tunnel switching of the magnetization can be described by the so-called one-domain approximation, when the total magnetization vector M is taken as a main dynamic variable with fixed absolute value M. Then the total energy density, or the anisotropy energy E, is obtained from the spin-Hamiltonian H using a spin coherent state n) chosen along the direction n [332,333] ... 

In practice, decay of the spin coherence during the delay time t,i and finite optical depth flatten and broaden the anti-Stokes pulse, reducing the total number of anti-Stokes photons which can be retrieved within the coherence time of the atomic memory. For weak retrieve laser intensities, the total photon number per pulse increases with increasing laser power because the time required to read out the spin wave is longer than the characteristic decoherence time of our atomic memory ( 3gs, see Fig. 3 b). After accounting for dead-time effects, we find that once the retrieve laser power increases to 25 mW, all of the spin wave is retrieved in a time shorter than the decoherence time, resulting in a constant anti-Stokes number versus retrieve power. 

Radiation scattering by an assembly of centres is also characterized by another effect related to time fluctuations concerning either the sample or the incident radiation. In fact, in the course of time, the total spin state of the neutron-nuclei system may change, and the same remark applies to the orientations of the anisotropic polarizable elements. Thus, the cross-section of the assembly of scattering centres is averaged over a period of time. Two contributions appear. The first one, which is called coherent, reveals interference effects between scattered rays. The second one, which is called incoherent, is the sum of the cross-section of the various centres (considered as isolated). 

If all nuclear spins in the sample were in exactly the same field, this signal would not decay, as the name implies, but would persist "forever." In any real sample, though, local fields cause different nuclei to be in slightly different total fields, and their moments ft precess at slightly different frequencies. Thus, following a 90° pulse, the moments y initially precess coherently but eventually get out of phase with each other, causing M to "decay" to zero. 

The coherence transfer provides cross peaks which are antiphase for the various 7//-split components. The antiphase nature of the cross peaks then leads to partial or total cancellation of the cross peaks themselves, especially if they are phased in the absorption mode. This behavior can be simulated (Fig. 8.15) using appropriate treatments of the time evolution of the spin system, for instance using the density matrix formalism [17,18]. It is quite common that signals in paramagnetic systems... 

Suppose that we are talking about a double-quantum transition in which both the proton and carbon change from the a state to the p state. This transition is thus from the aH c state to the PuPc state ol l lc two-spin, four-state system. This transition corresponds to DQC. Likewise, if the proton flips from ft to a while the carbon simultaneously flips from a to P, we have a zero-quantum transition (P ac to a Pc) because the total number of spins in the excited (ft) state has not changed. This transition corresponds to ZQC. What can we say about these mysterious coherences In Section 7.10, we encountered ZQC and DQC as intermediate states in coherence transfer, created with pulses from antiphase SQC ... 

In the case of lx, the central spin echo (r-180-r) leads to Vch evolution for a total time of IIJ, which moves lx to 2Iy Sz and on to - x. The central 180° pulse on H must be taken into account, but we consider it as if it happened at the beginning of the evolution, when we have lx, so it has no effect. Thus, the overall effect of the BIRD element is exactly the same as a 180° pulse on the / axis for the 13C-bound protons, and it has no effect on the 12C-bound protons. This will reverse the sense of the coherence helix in the NMR tube for the 13C-bound protons only, allowing the second gradient to straighten them out while it further scrambles the 12C-bound protons. 

TOCSY (total correlation spectroscopy) is an extension of the COSY experiment, in which the coherence transfer is not limited to a single jump from one proton to another via a J coupling. Instead, coherence is spread out over an entire spin system of coupled protons via multiple /-coupled jumps. For example, in a string of carbons CHa-CHb-CHc-CHd, coherence can be transferred by the TOCSY mixing sequence from Ha to Hc or from Ha to Hj. Thus, crosspeaks will be observed at F% = va and I = i b, vc or (Fig. B.5). 

The restoration process of the spin magnetization toward the thermal equilibrium is called paramagnetic relaxation. It can be divided into two categories longitudinal relaxation and transverse relaxation. The z-component of the total magnetization is restored by the former relaxation, while the coherence in precessing on the xy-plane is destroyed by the latter relaxation. 

On timescales of less than or equal to that of spin-spin relaxation (T2) processes occur. T2 characterises the loss of phase coherence of the individual spin isochromats within the spin ensemble comprising the total magnetisation vector M0. A spin isochromat represents a group of spins that experiences the same homogeneous magnetic field and which, therefore, behaves in the same... 

In this chapter multiple-pulse sequences for homonudear Hartmann-Hahn transfer are discussed. After a summary of broadband Hartmann-Hahn mixing sequences for total correlation spectroscopy (TOCSY), variants of these experiments that are compensated for crossrelaxation (clean TOCSY) are reviewed. Then, selective and semiselective homonudear Hartmann-Hahn sequences for tailored correlation spectroscopy (TACSY) are discussed. In contrast to TOCSY experiments, where Hartmann-Hahn transfer is allowed between all spins that are part of a coupling network, coherence transfer in TACSY experiments is restricted to selected subsets of spins. Finally, exclusive TACSY (E.TACSY) mixing sequences that not only restrict coherence transfer to a subset of spins, but also leave the polarization state of a second subset of spins untouched, are reviewed. 

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