The Effect of a Radio Frequency Pulse

During the period r, typically a few microseconds, is essentially constant, so Eq. 11.16 is applicable. The argument in the exponential becomes 

For a weakly coupled system of JV nuclei of spin /j, we can easily obtain explicit expressions for the exponential operators in Eq. 11.27 by applying Eq. 11.25 and the expansion ofEq. 11.20  

For manipulations of the density matrix by Eq. 11.27, it is convenient to express Eq. 11.29 in matrix form  

In accord with Eq. 11.28, the entire matrix R = exp(i0Fx) is obtained by taking the product of the matrices of Eq. 11.30 for each spin. This procedure will become clearer in the following sections. 

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The effect of a radio frequency pulse is to mix the a and p states so that a superposition of states is obtained ... 

The Bloch simulator module in NMR-SIM enables the offset dependence between the frequency of a pulse and the resonance frequency of an uncoupled single spin to be visualized graphically in a manner similar to the diagrams in the literature. Essentially the Bloch equations describe two simultaneous processes the effect of a radio frequency pulse on a macroscopic magnetization vector and the relaxation of the macroscopic magnetization back to its equilibrium value with the assumption that the Ti and T2 relaxation can be treated as a simple first order process. The NMR-SIM Bloch... 

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