Multi-pulse sequences from magic echoes

During the spin-lock period of duration 4r the secular dipolar Hamiltonian H is scaled by the factor —1/2 (cf. Section 3.4) so that the Hamiltonian averaged over the echo time = 6 vanishes [Rhil], 

The factor—1/2 is obtained from the second Legendre polynomial Fa = (3cos 0 — l) for the angle 0 = 90°, which the quantization axis of the spins forms wiA the Bq held during spin locking. As a result of self-compensation of the dipolar interaction in the different evolution intervals, the initially excited coherences are completely refocused under the magic echo. Another echo arises after half the echo time during the spin-lock 

In order to demonstrate the salient features of the technique, the pulse sequence of Fig. 8.8.1 is considered. If H denotes the average Hamiltonian of order zero, the density operator describing the FID, which is detected stroboscopically at times t = nt, is given by 

The magic-echo frequency-encoding method of Fig. 8.8.1 has been demonstrated on a phantom of adamantane and hexamethylbenzene [Mat 1 ]. The spatial resolution achieved was better than (100 p,m) . For both materials the H linewidth at half-height is about 15 kHz without homonuclear decoupling. 

In order to preserve the effect of the gradients on the evolution of magnetization in a time-suspension sequence, the gradient pulses must be applied with alternating polarity in successive free-evolution windows of the magic-echo sequence. In this case, the evolution of the density operator can be expressed similar to (8.8.2), 

---