Algebraic analysis of some double-resonance experiments

Abstract

The algebraic method of analysis is applied to three double-resonance experiments: (1) on-resonance spin decoupling spin ½ AX systems; (2) on-resonance cross-polarization spin ½ AX, AX₂, and AX₃ systems under mismatched rf fields; (3) refocused J cross-polarization (RJCP) spin ½ AX, AX₂, and AX₃ systems. In each case, all the coherences created and their time dependence are derived. All three situations are shown to involve the creation of zz order, and zero- and double-quantum coherences. The mechanism of the RJCP sequence is shown to involve rotations in two-dimensional operator spaces, and a new recipe is presented for purging coupled RJCP spectra.