Z magnetization

In this equation, 01 is the ifeqiieney of the RF irradiation, oiq is the Lannor ifeqiieney of the spin, is the spm-spm relaxation time andM is the z magnetization of the spin system. The notation ean be simplified somewhat by defining a eomplex magnetization, AY, as in equation (B2.4.3). 

A simple, non-selective pulse starts the experiment. This rotates the equilibrium z magnetization onto the v axis. Note that neither the equilibrium state nor the effect of the pulse depend on the dynamics or the details of the spin Hamiltonian (chemical shifts and coupling constants). The equilibrium density matrix is proportional to F. After the pulse the density matrix is therefore given by and it will evolve as in equation (B2.4.27). If (B2.4.28) is substituted into (B2.4.30), the NMR signal as a fimction of time t, is given by (B2.4.32). In this equation there is a distinction between the sum of the operators weighted by the equilibrium populations, F, from the unweighted sum, 7. The detector sees each spin (but not each coherence ) equally well. 

Figure B2.4.6. Results of an offset-saturation expermient for measuring the spin-spin relaxation time, T. In this experiment, the signal is irradiated at some offset from resonance until a steady state is achieved. The partially saturated z magnetization is then measured with a kH pulse. This figure shows a plot of the z magnetization as a fiinction of the offset of the saturating field from resonance. Circles represent measured data the line is a non-linear least-squares fit. The signal is nonnal when the saturation is far away, and dips to a minimum on resonance. The width of this dip gives T, independent of magnetic field inliomogeneity.

In the absence of exchange (and ignoring dipolar relaxation), each z magnetization will relax back to equilibrium at a rate governed by its own T, as in (B2.4.44). 

In a selective-inversion experiment, it is the relaxation of the z magnetizations that is being studied. For a system without scalar coupling, this is straightforward a simple pulse will convert the z magnetizations directly into observable signals. For a coupled spur system, this relation between the z magnetizations and the observable transitions is much more complex [22]. 

In a coupled spin system, the number of observed lines in a spectrum does not match the number of independent z magnetizations and, fiirthennore, the spectra depend on the flip angle of the pulse used to observe them. Because of the complicated spectroscopy of homonuclear coupled spins, it is only recently that selective inversions in simple coupled spin systems [23] have been studied. This means that slow chemical exchange can be studied using proton spectra without the requirement of single characteristic peaks, such as methyl groups. 

These complications require some carefiil analysis of the spin systems, but fiindamentally the coupled spin systems are treated in the same way as uncoupled ones. Measuring the z magnetizations from the spectra is more complicated, but the analysis of how they relax is essentially the same. 

We can control the extent by which the -)-z-magnetization is bent by choosing the duration for which the pulse is applied. Thus the term 90° pulse actually refers to the time period for which the pulse has to be applied to bend the magnetization by 90°. If it takes, say, t fis to bend a pulse by 90°, it would require half that time to bend the magnetization by 45°, i.e., t/2 fis. A 180° pulse, on the other hand, will require double that time, i.e., 2t fjts and cause the z-magnetization to become inverted so that it comes... 

Clearly the extent to which the H nuclei line up along the x -axis (Ild) will depend on the duration of tu which in turn will determine the extent of the antiphase z-magnetization created by the second 90° H pulse. The... 

An alternative way of realizing an isotope filter is shown in Fig. 17.4b, where the 90° phase difference between the two proton magnetizations is exploited [18]. A second 90° j1 ) pulse (of same phase as the excitation pulse) at the end of the period r =l/2j leaves the heteronuclear antiphase magnetization of the X-bound protons unaffected, while the other protons are converted to z magnetization ... 

In the pulse sequence for a homonuclear COSY experiment, the first 90° pulse flips the z magnetization into the x direction and into the xy plane. Considering an AX spin system (one in which the nuclei have very different chemical shifts) having two doublets due to spin-spin coupling, the magnetization will include four components processing at different frequencies. During a... 

In a pulse NMR experiment, the z magnetization is flipped into the xy plane, and the individual transitions start to process. During the detection,... 

---