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By H b. 1855 Drinkwater

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Furthermore, it is an even function of ω as well. On the other hand, the imaginary part of the integral in Eq. 37, k q (ω) = Im = Im ⎧ ⎨ ∞ ⎩ 0 ⎧∞ ⎨ ⎩ 0 is an odd function of ω. 39) 18 2 Theoretical Principles In the high-temperature limit, the equilibrium⎥⎥ density matrix is proportional to −q q H0 . Thus, using Eq. 33, the double commutator Akp , Akp , σ0 = 0. Using this property in Eq. 37, one obtains dσ T (t) 1 =− dt 2 ⎥ ⎥ −q q Akp , Akp , σ T (t) − σ0 k jq ωpq q=−k p ⎥⎥ −q q Akp , Akp , σ T (t) k q ωpq .

B The scheme is based on the repetition of a composite pulse R shown here. 90, 180, 270 and 360≈ pulses are represented by white, black, dark grey and light gray rectangles, respectively. The labels at the top of each rectangle indicate the phases of the rf pulses it is straightforward to recognize from Eq. 17 that RZQ = ζMQ − μMQ , RDQ = ζMQ + μMQ . 19) θRMQ = RDQ − RZQ = 2μMQ . 2 Preservation of Relaxation Pathways However, the simultaneous application of continuous-wave rf fields to both I and S, in a fashion analogous to R1π experiments, would not preserve the interconversion between the multiple-quantum coherences.

The thick vertical dashed lines define a cycle of duration 8σR . The rightmost of these lines corresponds to a time point t within the first pulse of an HDR WALTZ-32 sequence, as explained in the text WALTZ-32 block. The function ϕk (t, σ ) (k = I, S) has a period 8σR with respect to σ (see Fig. 7). This yields jn+1 (t) = exp [−8σR /σex ] jn (t). Therefore one obtains from Eq. 34 μWALTZ (t) = MQ 1 2 θτ j0 (t) 2 ∞ n=0 e−8nσR /σex = j0 (t) 1 2 θτ . 36) In this way the multiple-quantum cross-relaxation rate is calculated under the assumption that the rf irradiation preceding the instant t is infinitely long.

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