Application of the product operator formalism to spin (I = ½) systems under a radio-frequency irradiation

Abstract

The product operator formalism has been developed to evaluate, in closed and analytical form, the time evolution for spin (I = ½) systems in the presence of rf irradiation. This development is based on the fact that the time evolution propagator for the spin systems can be decomposed completely and thoroughly into the order multiplication of a series of elementary propagators. The inherent advantages and characteristic features of the formalism have been retained. As applications of this developed formalism, the Raman magnetic resonance in a weakly coupled two-spin system and the spin-locking process in the AB strongly coupled two-spin system are treated in detail. This formalism also gives a method for the analytic calculation of the spin-locking process in the ABC strongly coupled three-spin system.