Effective nutation frequency

The effect of the decoupling power on the efficiency of recoupling can be seen in Fig. 4. As the nutation frequency increases, the efficiency of the rotating-frame... 

If the nutation frequency cui = is much larger than the resonance offset (given by COL - f2), then the effective Hamiltonian is approximated by ... 

The case of off-resonance pulses is a little bit more involved, since now the axis of nutation is given by the effective magnetic field in Equation (2.3.6) and, therefore, is not contained in the transverse plane. The extent to which this axis is tilted out of the transverse plane and the sense of the tilt is determined by the frequency offset ( >l — 2). Also the nutation frequency is no longer given by co = y Bi, but depends on the offset. It can be shown that the rotation operator describing such off-resonance pulse can be written as a product of five rotations about orthogonal axes [5] ... 

The opposite extreme regime, when co coq, involves the so-called soft or selective RF pulses. In this case, pulses of long duration and low power can be used to excite just one of the transitions, which is achieved by a suitable choice of the resonance offset (72) and also of the pulse length. The main aspect to be considered here is that each transition has associated with it a specific frequency and a different effective nutation fi equency, which depends on the values of I and m. For selective excitation of a transition between the levels m + and m, it is found that the ideal soft jr/2 pulse must be shorter than the corresponding hard itjl pulse (which excites all transitions) by a factor of -3-1) —m m 1). For excitation of just the central transition (1 /2 -1 /2) for half-integer spin nuclei, the... 

Quadrupole nutation NMR is a technique, introduced by Samoson and Lippmaa (27), where in a two-dimensional way the effect of the quadrupole interaction is separated from other line broadening interactions, simply by allowing the magnetization to evolve during an incremented periode tj, under the influence of a strong radio frequency field. 

The bifurcation scenario discussed above was actually observed in the experiment. Although a good qualitative agreement between theory and experiment was found [40], there are quantitative discrepancies. In the experiment, the measured onset of the nutation-precession motion turns out to be about 20% lower than predicted by theory. Moreover, the slope of the precession frequency versus intensity predicted by theory turned out to be different from that observed in the experiment. One of the two possible reasons could be the use of finite beam size in the experiment (that is typically of the order of the thickness of the layer), whereas in theory the plane wave approximation was assumed. Actually, the ratio 5 between diameter of the beam and the width of the layer is another bifurcation parameter (in the plane wave approximation, 6 oo) and was shown to play crucial role on the orientational dynamics [13]. There and in [44] the importance of the so called walk-off effect was pointed out which consists of spatial separation of Pointing vectors of the ordinary and extraordi-... 

The method is most appropriate when the spectmm is dominated by a single resonance, so has obvious application to samples in heavily protonated water but can be equally effective fcff organic solutions when a single dominant peak can be identified, such as a resolved methyl resonance for example. This must be placed on-resonance, and the smallest frequency separation between the anti-phase peaks in the nutation spectmm is then used in the appropriate calculation. The whole procedure is most conveniently executed through appropriate software routines, which may be supplied as standard by your instrument vendor. 

In the steady state experiments considered here, the competition between nutation and relaxation processes leads to the creation of a finite transverse magnetization < M > in the rotating frame. The amplitude and phase of relative to these of depend on the frequency difference (cOq-iOj ) and on the effective longitudinal and transverse relaxation times and T2 respectively. In the laboratory frame the transverse magnetization appears to undergo a forced precession at the frequency Mq/Zit, and consequently those physical observables of the system which depend on (M > and are modulated at the same frequency. 

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