Precess

Al.6.101) are precisely equivalent to these derivatives the rate of change of a population is proportional to the instantaneous coherence, a relationship which can be observed already in the vector precession model of the two-level system ( section Al.6.2.3). 

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

Magnetic resonance unaging, flow and diflfiision all rely upon manipulating spatially varying magnetic fields in such a maimer as to encode spatial infonnation within the accumulated precession of the magnetization. In... 

As before, we note that the resonance frequency of a nucleus at position r is directly proportional to the combined applied static and gradient fields at that location. In a gradient G=G u, orthogonal to the slice selection gradient, the nuclei precess (in the usual frame rotating at coq) at a frequency ciD=y The observed signal therefore contains a component at this frequency witli an amplitude proportional to the local spin density. The total signal is of the fomi... 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

These experiments yield T2 which, in the case of fast exchange, gives the ratio (Aoi) /k. However, since the experiments themselves have an implicit timescale, absolute rates can be obtained in favourable circumstances. For the CPMG experiment, the timescale is the repetition time of the refocusing pulse for the Tjp experiment, it is the rate of precession around the effective RF field. If this timescale is fast witli respect to the exchange rate, then the experiment effectively measures T2 in the absence of exchange. If the timescale is slow, the apparent T2 contains the effects of exchange. Therefore, the apparent T2 shows a dispersion as the... 

The vector L is so strongly coupled to the electrostatic field and the consequent frequency of precession about the intemuclear axis is so high that the magnitude of L is not defined in other words L is not a good quantum number. Only the component H of the orbital angular momentum along the intemuclear axis is defined, where the quantum number A can take the values... 

Vortex precession meters feature no moving parts and a relatively high frequency digital output. They are used in the measurement of gas and Hquid flows, generally in pipe sizes 80 mm and smaller. 

Fig. 17. Mixing of floating soHds in agitated tanks (a) no surface movement, full baffles width = T/12 (b) deep vortex, no baffles need high energy which causes tank to sway (c) precessing vortex, partial baffles width = T/50 and (d) submerged partial baffles.

Figure 1.1. Nuclear precession nuclear charge and nuclear spin give rise to a magnetic moment of nuclei such as protons and carbon-13. The vector n of the magnetic moment precesses in a static magnetic field with the Larmor frequency vo about the direction of the magnetic flux density vector Bo...

Relaxation refers to all processes which regenerate the Boltzmann distribution of nuclear spins on their precession states and the resulting equilibrium magnetisation along the static magnetic field. Relaxation also destroys the transverse magnetisation arising from phase coherenee of nuelear spins built up upon NMR excitation. 

Figure 4-4. (A) Magnetic moment vector i. precessing about applied field vector Hq. (B) Addition...

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