Near neighbor approximation in nuclear magnetic resonance

A new way to deal with the excitation by multiple effective RF fields with interference is presented using the coherent averaging theory. It significantly simplifies the calculation of the effect of RF interference that occurs in the excitations by periodic pulses and phase-incremented pulses (PIPs). This approach shows that each neighboring RF field contributes to an excitation profile an offset shift, which is termed the Bloch-Siegert offset shift (BSOS). The BSOS depends not only on the strengths of both RF fields that interfere with each other but also on their relative phase between the two RF fields. Consequently, it can be positive, negative, and zero. In addition, the BSOS is also inversely proportional to the frequency separation of the two RF fields. Therefore, only a few near neighbors need to be taken into account in most cases, resulting in a near neighbor approximation (NNA). The BSOS for two multiband excitation profiles, one by a periodic pulse and the other by a PIP, are calculated using the NNA. The results are in good agreement with the computer simulated ones.