Analytical Polarization and Coherence Transfer Functions for Three Dipolar Coupled Spins 1/2

Analytical polarization and coherence transfer functions are presented for a spin system consisting of three dipolar coupled homonuclear spins 1/2 under energy matched conditions. Based on these transfer functions, optimal durations of Hartmann-Hahn mixing periods can be determined for arbitrary dipolar coupling constants D₁₂, D₁₃, and D₂₃. In addition, the dependence of the transfer efficiency on the relative size of the dipolar coupling constants is illustrated.