This subproject is one of many research subprojects utilizing theresources provided by a Center grant funded by NIH/NCRR. The subproject andinvestigator (PI) may have received primary funding from another NIH source,and thus could be represented in other CRISP entries. The institution listed isfor the Center, which is not necessarily the institution for the investigator.In this work, we treat the general problem of relaxation during an adiabatic radiofrequency pulse. In the NMR literature, relaxation during a RF pulse has either been neglected or avoided using the so-called 'delta function approximation' where relaxation during the short time of the pulse is assumed to be negligible. However, it is becoming more and more common to use RF pulses having durations on the order of many milliseconds, where there is an explicit time-dependence in the first rotating frame. The result of these developments is that the time-dependence of relaxation during the RF pulse becomes important for the successful analysis of NMR data. In this work we detail some of the theoretical concepts for treating NMR relaxation that we have found necessary in developing the successful fitting to data of NMR experiments where the time dependence results from the use of adiabatic pulses. We explicitly treat the case of identical spins , then the situation of two distinct spins both for the case of the dipolar relaxation mechanism and for two site chemical exchange.
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