J‐coupling and chemical‐shift evolution during I‐spin irradiation of ImSn systems: Product operator solutions and applications

Abstract

AbstractWe previously obtained exact solutions for the time dependence of the density operator in weakly coupled spin‐½ ImSn systems during arbitrary RF irradiation of the I spins. The solutions for the density operator were written as explicit linear combinations of its product operator components (i.e., the operator basis set consisting of direct products of the I‐ and S‐spin operators). Other solutions for the product‐operator evolution of the density matrix have considered either evolution in the absence of RF irradiation or the case where the RF is sufficiently strong that J‐coupling effects can be ignored. The present solutions therefore extend the range of applications that are accessible to the product‐operator formalism and vector pictures of nuclear spin evolution. Here, we derive the solutions for an IS system in detail to illustrate the simplicity of the formalism and supplement our previous, but more general, abstract treatment of the subject. We then outline how the formalism is applied to the ImSn case. We also briefly discuss the rigorous vector picture that can be associated with the states of the system at each time. The solutions provide new insight into the combined effects of RF irradiation and J‐coupling. Applications include (1) novel methods for calibrating an RF channel for insensitive I spins by observing large signals from multiple quantum coherences with the S‐spin channel, and (2) new RF pulses for achieving selective coherence transfer. © 2002 Wiley Periodicals, Inc. Concepts Magn Reson 14: 287–307, 2002.