We first introduce an alternative way to study the insensitive nuclei enhanced by polarization and distortionless enhancement by polarization transfer NMR experiments with the product operator descriptions for weakly coupled I (I=1/2, S=1/2) spin systems as a quantum controlled not gate and a not gate, respectively. In this framework we apply the density matrix operators obtained from the analytical descriptions of the mentioned pulse sequences by using product operator formalism step by step on the NMR spin product states represented in Dirac's notation.
Product operator theory was often used to describe analytically multipulse NMR experiments for weakly coupled spin systems. In this study first we introduce the descriptions of subspectral editing with a multiple quantum trap NMR spectra for IS_n I=1 /2, S=5/2 with n=1, 2, 3) spin systems by using product operator formalism. These theoretical investigations lead us to form the general expressions for the intensities of the spin -1/2 nuclei coupled to the nuclei with spin ≥5/2. The obtained results can be used for the spectral editing in both liquid-state and solid-state NMR experiments. Furthermore, in order to satisfy the obtained analytical expressions for signal intensities we add the presentation of analytically description of subspectral editing with a multiple quantum trap sequence for weakly coupled IS (I=1/2, S=7/2) spin system.
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