Nutation frequency

The analytic evaluation of the density matrix requires the diagonalization of Hi, which can be easily performed for the two extreme cases, a>r( Qg. Indeed, in the case of a low rf-field, only off-diagonal terms related to the CT are retained in the H Hamiltonian (39), which thus behaves like a fictitious spin-1/2 operator, affecting only the CT coherences /1 io- These coherences are thus selectively excited with the nutation frequency ... 

The spin-locking and CP behavior of the most commonly used SQ coherence (CT) in quadrupolar nuclei under static and MAS conditions has been described in detail by Vega using the fictitious spin-1/2 approximation [223]. In a static sample, the Hartmann-Hahn matching condition requires that co = nut where co ut is one of the nutation frequencies associated with the SQ coherence of the quadrupolar S spin (see Sect. 2.3.4). In the simple case of on-resonance SQ-CP this translates to [224]... 

The Hartmann-Hahn MQ-CP transfer can be achieved when the rf frequency of spin I in the rotating frame is sufficiently close to one of the SQ or MQ nutation frequencies of spin S, co/ut = oJlf. In the case O/ > co/f, the nutation frequency for a symmetric MQ coherence of order p is given by [222, 229]... 

In Section 2.2.6, the nutation frequency of a quadrupolar nucleus was seen to vary from (I + /2)v] when vi << vq to V when V >> vq. The nutation spectra display distinct features in the region where vi vq. Simulation of nutation behaviour has shown that the useful range of rf field-strengths lies with vq/vi in the range 0.05-1. The distinct features of nutation spectra allow the quadrupole parameters to be obtained. This means that only quadrupole frequencies up to a certain limit are accessible with currently available rf-fields of 500 kHz in specially dedicated probeheads, and in fields of around 100 kHz in most commercially available systems. This constraint especially limits the investigation of spin I = 3/2 nuclei such as Na. 

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... 

During a period of evolution in which multiple-quantum states are present, the magnetization acquires a modulation due to the nutation frequency of the MQCs. Thus, signals which are due to single sites during other evolution periods will have the same spectral frequency in a multiple-quantum domain as those signals which had passed through the same MQC. This can therefore easily be read in a multi-dimensional spectrum as a correlation between these nuclear sites. In addition, a multiple-quantum domain as part of a multi-dimensional spectrum removes the auto-correlation peaks on... 

Nutation frequency measurement Peter Wu and Gottfried Otting have recently described a technique that can quickly and accurately yield the 90° pulse width via a single acquired transient. The concept is to measure the... 

Nutation NMR spectroscopy was introduced by Samoson and Lippmaa for the study of half-integer quadrupolar nuclei. For quadrupolar nuclei in the rotating frame, the nutation frequencies and amplitudes of the excited Zeeman... 

Here we have assumed exact MAS in the second step single-transition operators and the DQ nutation frequency... 

A new approach to markedly reduce RF power for observed nuclei during H-homonuclear decoupled CP has been described Nishimura and Naito. The reduction of RF power to satisfy the Hartmann-Hahn matching condition for observed nuclei and homonuclear dipolar decoupling at H nuclei were achieved simultaneously based on time averaging of nutation frequency of H nuclei by frequency switched Lee-Goldburg decoupling with unequal duration times. The RF nutation frequency and RF field for observed nuclei were shown experimentally to be reduced by factor 3 and 10, respectively, at NMR signals. 

Now let us consider the power required to saturate a Rydberg transition. This can be obtained by saying that the monochromatic field irradiating the atom must produce a nutation frequency for the atomic dipole, qao, equal to the radiative decay rate, i.e-. 

Spectra extracted from the complete data set of a high power 200 mW) experiment at K-band are shown in Fig. 2a. The solid line is obtained from the initial amplitudes of transient nutation signals. The broken line has been obtained from the Fourier coefficients of the nutation frequency where only times longer than 900 ns after the laser pulse have been retained in the transformation of the transients. Both spectra - although totally different - belong to the same spin pair P700A1. They can be simulated quite satisfactorily (Fig. 2b) The early... 

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