Free precession

Carr H Y and Purcell E M 1954 Effects of diffusion on free precession in nuclear magnetic resonance experiments Rhys. Rev. 94 630-8... 

In cases where ideal (i.e., instantaneously short) rf pulses are used, it is useful instead to use a so-called toggling frame approach where the Hamiltonian by each pulse is toggled to another frame. For the case where N ideal rf events have occurred, the Hamiltonian for the free precession period following the Mh pulse is described by... 

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... 

The simulation contains two types of events that should be translated into equations the free precession and the exchange event. A third operation, the calculation of the FID points, does not influence the density matrix, but its importance explains why it should be dealt with in detail in the following sections. 

Figure 14.8 (a) General scheme of two-dimensional multiple-quantum (MQ) spectroscopy. During both intervals of free precession (MQ coherences during tx and SQ coherences during t2) dipolar decoupling can be achieved by MAS. Possible pulse sequences used for excitation/reconversion of MQ coherences are (b) broadband... 

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. 

POMA A complete mathematica implementation of the NMR product-operator formalism—Guntert et al. JMR 101A, 103-105 (1993). POMA is a flexible implementation of the product operator formalism for spin-1/2 nuclei written for Mathematica. It provides analytical results for the time evolution of weakly coupled spin systems under the influence of free precession, selective and non-selective pulses, and phase cycling. As part of Mathematica, it requires a license, but the source code is free. Mathematica also provides a framework for visualizing and storing results. 

One specific sub-matrix, Lo, operating on the basis operators Tg, ..., T0 for an N-site jump during free precession can be evaluated analytically because of its high degree of symmetry. That is,... 

In this case a two-axis jump process is studied. The two-site jump around the first axis is characterized by a rate constant k, whereas the rate constant for the jump around the second axis is AT During free precession only the + IQ coherence is of interest and therefore the matrix of interest is... 

In Table 11.1 we sketch the form of the density matrix for the two-spin system to show the significance of the elements. Px —P4 refer to the populations of the four states, I and S represent single quantum I and S transitions, and Z refers to zero quantum transitions and D to double quantum transitions. We saw in Eq. 11.9 that an off-diagonal element pm is nonzero only if there is a phase coherence between states m and n, and in Eq. 10.19 we saw that pmn, evolves with a frequency determined by the difference in energies Em — En. Thus, these off-diagonal elements represent not only transitions, but single quantum, double quantum, and zero quantum coherences, which evolve in free precession at approximate frequencies of v, vs, vt + vs, and vt — vs. In Eq. 11.53 we see that p(r) has... 

Coherent transfer experiments can roughly be divided into two classes pulse-interrupted free-precession experiments and Hartmann-Hahn-type experiments (Ernst et al., 1987). Examples of homo- and heteronuclear pulse-interrupted free-precession coherence transfer are COSY (correlation spectroscopy Aue et al., 1976), RELAY (relayed correlation spectroscopy Wagner, 1983), and INEPT (insensitive nucleus enhancement by polarization transfer) transfer steps (Morris and Freeman, 1979 Burum... 

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