RAFFn relaxation rate functions

In the present study we derive expressions for relaxation rate functions due to dipolar interactions between identical spins in the rotating frames of rank greater than or equal to 3. The rotating frames are produced due to fictitious magnetic field as generated by amplitude and frequency modulated radiofrequency (RF) pulses operating in non-adiabatic regime. This solution provides a means for description of the relaxations during method entitled Relaxation Along a Fictitious Field (RAFF) in the rotating frame of rank n (RAFFn), in which a fictitious field is created in a coordinate frame undergoing multi-fold rotation about n axes (i.e., rank n). We validate the proposed model by comparison with the accepted trigonometric relations for relaxation rates between tilted frames. The agreement between the proposed model for RAFF3 and the trigonometric model is excellent.