Zq

N(faa)

SQ*(S2)

faIfaS

l dq

SQ(I2)

SQ(S2)

N(fafa)

where Nrepresents the population of an energy state, SQ represents single-quantum (observable) coherence, DQ represent double-quantum coherence, and ZQ represents zero-quantum coherence. For example, SQ*(I2) is the complex conjugate of the coherence for the aIfaS ^ faIfaS transition, with spin I changing state and spin S remaining in the fa state. The spectrum (observable SQ transitions only) consists of four lines (two doublets): I1, I2, S1, and S2.

For a 13 C-1 H system at equilibrium, we have

corresponding to the energy diagram shown in Figure 10.37 (units of radians/s). For I = 1H and S = 13C, the energy separation for the 1H transitions is about four times as large as the energy separation for the 13C transitions. As before, we factor out the N/4, separate out the identity matrix, and factor out the e. Omitting the identity matrix and the Ne/4 factor, this gives

eq
0 0

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