S-spin magnetization

Interaction of an electron s spin magnetic moment with the magnetic field it experiences by virtue of its motion relative to the external electric field (spin-orbit term). 

ESR transitions are due to the interaction of the electron s spin magnetic moment fis with the oscillating field of the incident microwave radiation. The experimental setup is such that B, is perpendicular to B0, so that the selection rules are determined by the integral... 

Fig. 2. A 2D SLF pulse sequence (A) with S-spin magnetization evolution (B) subject only to heteronuclear dipolar couplings in the q period and detection of chemical shift spectrum in the 2 period. Various multiple pulse (MP) sequences can be used to suppress dipolar coupling among I spins in the laboratory frame during the h period, which enables line-narrowing in the I-S dipolar coupling dimension (i.e., the a>i frequency dimension of the 2D spectrum). This experiment under MAS can be used for separating I-S dipolar sideband patterns by isotropic chemical shifts the re-pulse and the start of the acquisition need to be synchronized with rotational echoes. Other aspects of this pulse sequence are similar to the SLF sequence in Fig. 1.

As discussed above, the magnetization has been represented as the corresponding operator, Iz. Likewise for the S-spin magnetization... 

It must be remembered that the populations used to derive these equations are really the deviation of the populations from their equilibrium values. As a result, the I and S spin magnetizations should properly be their deviations from their equilibrium values, 7° and S° the equilibrium value of 27 S is easily shown, from its definition, to be zero. For example, Eq. [14] becomes... 

What this says is that if the S spin magnetization deviates from equilibrium there will be a change in the I spin magnetization at a rate proportional to (a) the cross-relaxation rate, aIS and (b) the extent of the deviation of the S spin... 

The S spin magnetization returns to its equilibrium value with what appears to be an exponential curve in fact it is the sum of two exponentials but their time constants are not sufficiently different for this to be discerned. The I spin magnetization grows towards a maximum and then drops off back towards the equilibrium value. The NOE enhancement is more easily visualized by plotting the difference magnetization, (I, - /z°)//z°, on an expanded scale the plot now shows the positive NOE enhancement reaching a maximum of about 15%. 

Here, Gx dephases the S spin magnetization present at the end of tx and, after transfer to the / spins, G2 refocuses the signal. An extra 180° pulse to S in conjunction with the extra delay xl ensures that phase errors which accumulate during G] are refocused G2 is contained within the final spin echo which is part of the usual HSQC sequence. The refocusing condition is... 

On the basis of your answers to (i) and (ii), suggest a suitable phase cycle, different to that given in the notes, for eliminating the contribution from the equilibrium S spin magnetization. 

In double resonance experiments, rf-pulses or pulse sequences are applied not only to the resonating 7-spins, but also to the non-resonating S-spins. Magnetic interactions between the resonating and the non-resonating nuclei, especially the heteronuclear magnetic dipole-dipole interaction, can be studied selectively by double resonance techniques. 

Assuming a good HH match, very long relaxation times, and that the protons outnumber the carbons ( C), i.e., Ns/Nj 0, the magnitude of the S spins magnetization is described as... 

An electron s spin magnetic moment is plus or minus the value of the Bohr magneton (plus for spin up and minus for spin down). 

If spin-lattice relaxation can be neglected, the S-spin magnetization obtained from the n contact will be ... 

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