Transverse /-spin magnetization

The picture set up above is complete when the gradients are the sole source of spin evolution, there is no relaxation and the spins do not move. In the liquid state the gradients can often be made sufficiently strong that relaxation and chemical shifts are minor complications and the limits to resolution and image distortions arise from limited NMR sensitivity and molecular transport. For rigid solids, molecular transport is not an issue, but the short lifetime of the transverse spin magnetization is. 

T, Transverse (spin-spin) relaxation time for x,y-magnetization... 

Fig. 10. The pulse sequence for the WISE experiment.21 This two-dimensional experiment separates H wideline spectra according to the isotropic l3C chemical shift of the 13C each H is bonded to. An initial H 90° pulse creates transverse H magnetization that is allowed to evolve in t. A short cross-polarization step then transfers the remaining H magnetization to the nearest 13C spin, i.e. the bonded one. The resulting 13C transverse magnetization is then allowed to evolve in ti under magic-angle spinning, where an FID is recorded.

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. 

The ESE intensity does not depend on t if the precession frequency of each electron spin does not fluctuate during the time interval 2t. However it does more or less fluctuate under the influence of surrounding spins etc., the precession of the spins looses coherence. The refocussing becomes more and more imperfect and the ESE intensity becomes weaker and weaker as the time elapses after the 90° pulse. This behavior of the spin magnetization is called phase relaxation. Both the free induction decay and the phase relaxation are called transverse relaxation. 

A development in the theory of nuclear relaxation in macromolecules by paramagnetic ions has been suggested by Gueron. (675) In the case of heme proteins there is a net polarization of the iron electronic spin magnetic moment which is oriented along the direction of the magnetic field. Modulation of this dipolar field due to the spin polarization (Curie spin) by rotational diffusion introduces an additional term into the expression for transverse relaxation [equation (18)] giving ... 

The computational procedure follows closely the steps of an actual m.p. experiment see Fig. 1. The spin system, which is initially in thermal equilibrium, is hit by a preparation pulse Pp. Thereafter, one component of the transverse nuclear magnetization created by Pp, say My, is measured and the measurement is repeated at intervals of the cycle time The resulting time series My(qtJ,q = 0,...,(2 " - 1), if Fourier transformed. For simulations we accordingly first specify the initial condition of the spin system, that is, the initial value of the spin density matrix g(t) in the rotating frame. Our standard choice Pp, = P implies p(0) fy == the sum running over k = We then follow the evolution... 

We have performed a model calculation of the electron structure of AF Cr for two types of the unit cell extended along the axes Y and Z, which corresponded, respectively, to the longitudinal and transversal spin density waves (5PW and SDWj ). Recall that the magnetic moment of the system was Z-directed. Additionally, we have varied the number of atoms per unit cell N = 2,4,8,20, and40, which corresponded to = 0,0.5,0.25,0.1,0.05. In all instances the same values of F(r) iuid Ao(r) were used. The spin-polarizing exchange part of the potential AF(r) for different atoms of the unit ceil was defined according to (18). The number of terms in expansion (10) amounted to 12N. 

In liquid crystals the proton resonance line width and the related effective transverse spin relaxation time T2 depend on the angle 9 between the magnetic field and the director n, which is described approximately... 

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