Density matrix approach to nuclear spin relaxation

On the other hand, after a selective pulse applied to a given transition connecting the levels specified by m and i — 1, the deviation density matrix contains coherences only between those levels. For I = 2i 12 and considering a selective nll)-x pulse applied to the central transition (1/2 —y -1/2), the deviation matrix is proportional to a fictitious spin-1/2 operator ly, whose form is analogous to the one given in Equation (2.9.12). 

The time evolution of such operator can be calculated from Equation (2.9.15), and the resulting FID from the calculation of the expectation value Ix + ily). In this case, it is found that the FID involves only one oscillating signal with frequency col. Therefore, the NMR spectrum now contains only one line, centered at frequency col, but with intensity reduced as compared to the corresponding line detected in the non-selective case [18,23], 

10 DENSITY MATRIX APPROACH TO NUCLEAR SPIN RELAXATION 

The relaxation processes can be also described using the density operator formalism. To account for the longitudinal and transverse relaxations for a simple spin 1 /2 system in a phenomenological way [24], the relaxation effects on the time evolution of the density matrix, p t), can be estimated by  

For single spin 1/2 systems, 7]y is related to the relaxation times by  

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Density matrix approach to nuclear spin relaxation... 

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