Magnetization modes in weakly coupled spin systems without magnetic equivalence

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Abstract
The concept of magnetization modes in longitudinal nuclear magnetic relaxation of spins 1/2 is reconsidered with regard to the total spin inversion operator Λ. It is shown that simplifications in the transition probability matrix can only occur through this operator: a two block separation is achieved provided that (i) relaxation takes place solely by intramolecular dipolar and random field interactions and (ii) the investigated spin system is weakly coupled. In the case of such a system involving n nonequivalent spins, a method is given for constructing 2n−1 antisymmetric (with respect to Λ) independent magnetization modes and 2n−1−1 symmetric independent magnetization modes from properly selected sums and differences of standard intensities relative to lines occupying symmetrical positions within each multiplet (a standard line intensity is defined as the difference between populations of the levels connected by the considered transition). The disconnected evolution matrices relevant to these two type of modes are easily set up from the initial transition probability matrix by means of transformation matrices deduced from the magnetization mode construction procedure. The effects of the inverting and observation rf pulses (selective, semiselective, and nonselective) are thoroughly studied. In particular, it is demonstrated that (i) symmetric modes can only be created by a selective pulse and (ii) the magnetization modes, as defined above, are directly observed by semiselective pulses or nonselective pulses of small flip angle. Otherwise mixing occurs.