Precession signal, free

We consider systems whose Hamiltonian may be split into an unperturbed term with a continuous spectrum and a perturbation causing the evolution towards equilibrium. We shall first consider observables which do not commute with 3 0. A beautiful example of such a phenomenom is the free precession signal studied in detail by Lowe and Norberg.25 Let us recall... 

For the Zeeman interaction of the nuclear spins with the static magnetic field, the Hamilton operator is time-independent, Hz = — yljfio = coqIz. Then the evolution operator (2.2.47) applies and (2.2.64) reduces to the free precession signal, which eventually determines the FED via the expectation value of the transverse angular momentum operators and Iv... 

Another development in modulation as applied to NMR is time-share modulation (Anderson, 1962 Grunwald, et al., 1962 Baker, et al., 1965 Boden, et al., 1968). This is a variation of amplitude modulation (AM) in which the transmitter produces an rf pulse while the receiver is pulsed off. Then, when the rf pulse is off, the receiver is turned on to detect the NMR free precession signal. Although time-shared modulation is a hybrid between cw and pulse methods, we discuss it because the apparatus for pulse NMR can be used for it with trivial modifications. 

The next step in approximation of the theory for EPR measurements was done by Atsarkin and co-workers in [138]. Basing on Fel dman s results, the researchers studied dipolar broadening and spin exchange narrowing of EPR lines from the paramagnetic centers distributed on the solid surface, and a simple formula for a signal of free precession S(t) was expressed [138] ... 

Two types of spectrometer are used to display nitrogen resonances the continuous wave (cw) spectrometer, which detects the absorption line or its derivative, and the pulse apparatus on which free precession decays or echo signals are observed. 

The problem is quite different with pulse spectrometers, for which the prospects are good free precession and echo signals are rather long as compared to those of protons in solids and they can readily be fed into a standard digital memory oscilloscope with an access time of about 40 microseconds. The gain is considerable 15> 161 provided good sample temperature and spectrometer frequency stabilizations are achieved. 

The free precession of the spin system is observed via the voltage induced in a coil wound around the sample. The signal due to a time-... 

Consider the free procession signal acquired as a function of time t after the spin-echo formation at time t. We shall presume that the sole term acting in the Hamiltonian after the echo center is due to the Larmor precession at frequency in the uniform field, where the use of the subscript i allows for the range of chemical shifts in the NMR spectrum. This precession contributes an evolution operator exp(iWo,t ->, ) to the density matrix so that we can rewrite Eq. (39) as... 

Additional gain in the signal-to-noise ratio can also be obtained by synchronous detection [63] or by acquiring multiple echoes during the free precession period of the observable single-quantum coherence (MQ-QCPMG-MAS experiment proposed by Vosegaard et al. [64]). 

Fig. 3.3 The precessing magnetization will cut a coil wound round the x axis, thereby inducing a current in the coil. This current can be amplified and detected it is this that forms the free induction signal. For clarity, the coil has only been shown on one side of the x axis.

So, if we have created some transverse magnetization (for example by applying a 90° pulse) overtime relaxation will cause this magnetization to decay away to zero. The free induction signal, which results from the magnetization precessing in the xy plane will therefore decay away in amplitude. This loss of v- and y-magnetization is called transverse relaxation. 

This section focuses on the coupling evolution that occurs during the pulse sequences of heteronuclear correlation experiments. Because polarization transfer is a requirement of intensity optimized heteronuclear correlation spectroscopy this section also acts as a short introduction to coherence transfer by polarization transfer. A coherence transfer from a sensitive nucleus, e.g. in most experiments, to a nucleus contributes a gain of signal intensity. To obtain the required antiphase coherence for the transfer step the coherence must evolve exclusively by heteronuclear coupling during a free precession periods. This can only be assumed in theoretical spin systems. In real samples three aspects make this ideal approach more difficult ... 

Filter elements have been developed, not just for coupling evolution, but also for chemical shift selection [5.215 - 5.221]. An early example was the jump-return method for solvent signal suppression. Check it 5.2.3.3, whereby the resonances at a given chemical shift and related multiples were suppressed. In common with the z-filter for zero-quantum suppression, the CSSF (Chemical 5hift iSelective Filter) element uses different free precession periods to give varying degrees of chemical shift evolution for each scan in a multiple scan experiment. 

Relaxation in Coupled Spin Systems. - The ability to transfer coherences between different nuclei in homo- and heteronuclear spin systems is one of the cornerstones of NMR. The transfer of polarization from I = (1/2) to enhance the signal of low-gyromagnetic ratio S = (1/2) nuclei has become routine. In solution state the majority of these methods employ free-precession type techniques such as INEPT where polarization transfer from one spin to another is mediated via the scalar coupling. The majority of these techniques are designed for spin-half systems and have shown particular utility in the study of structure and dynamics of biomolecules labeled with C and N. The use of INEPT for achieving polarization transfer in systems of scalar coupled quadrupolar nuclei has also been investigated. ... 

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