Precession rate

In order to analyze these data, the frequency shift of geffectivecan be calculated by averaging over all orientations the anisotropic shift derived from a static spin Hamiltonian [67]. This treatment is based on the assumptions that molecular motion neither changes the spin precession rate nor perturbs the states and, thus, that the center of gravity of the spectrum is invariant even in presence of some motional averaging. For the allowed 11/2) <-> <-l/2 transition under perturbation theory, with expressions valid up to the third order, this shift is given by [47] ... 

Figure 9.16. The path of the Planck scan circle center when the precession angle is 15° and the precession rate is 10 cycles per year. The difference between the Northern and Southern loops of the cycloid causes the asymmetry in the coverage pattern seen in Figure 9.15.

In the motional narrowing limit (co0tc 1, where co0 is the Larmor angular precession rate), the longitudinal and transverse relaxation times, Tj and Tz, in... 

It cannot be emphasized too much that the resonant frequency in NMR is proportional to the magnetogyric ratio, y, and to the laboratory magnetic field strength, B0. This relationship forms the basis of nearly every phenomenon observed in NMR. There are two ways to measure the precession rate the angular velocity, co0, in units of radians per second and the frequency, v0, in units of cycles per second or hertz. In this book we will use frequencies in hertz. This frequency is sometimes called the Larmor frequency, and the zero subscript refers to this fundamental frequency, which results from the laboratory magnetic field interacting with the nucleus magnetic field. 

Note that we use A v to refer to the rotating-frame frequency (sometimes called the resonance offset). This is the difference between the Larmor frequency and the reference frequency v0 - vr. The above equation shows that the same physical law expressed in the equation on the left-hand side (precession rate is proportional to y and to B0) is operating in the equation on the right-hand side (resonance offset is proportional to y and to fires) in the rotating frame of reference, as long as we introduce the pseudofield. In the NMR spectrum, A v is the distance from the center of the spectral window to the NMR peak (Fig. 6.2), also represented as 2 in units of radians per second. If the peak is in the downfield half (left half) of the spectrum, the Larmor frequency is greater than the reference frequency ( v0 > vr) and we have a positive resonance offset (A v > 0). This corresponds to the motion of the net magnetization... 

For example, on a 600-MHz spectrometer XH SQC precesses at 600 MHz, 13C SQC pre-cesses at 150 MHz, and H- C DQC precesses at 750 MHz. This makes sense because we are talking about a transition in which both XH and 13 C change from the a to the p state. Zero quantum coherence behaves in a similar way, but the precession rate is the difference between the two SQ precession frequencies ... 

EXAMPLE 8.4 If the methylene hydrogens were in the M = 0 state, what effect would they have on the precession rate of the methyl hydrogens ... 

Low-spin iron(III) ions have an electron hole in the t2g orbitals. Therefore, these centers have S = 1/2 and spin-orbit interaction contribntes considerably to the magnetic hyperfine field. Low-spin iron(III) componnds in solution always show a rather complicated magnetic Mossbauer pattern at temperatures around 4.2 K and low external fields, which means that the relaxation rate of these centers is lower than the nnclear precession rate of 10 s. Sometimes a magnetic sphtting is observed even at 77 K. Therefore, in order to pin down 8 and A g, it is advisory to measure between 100 and... 

Following an rf pulse, because the tensor orientations of each crystallite are different, the resonant frequency for each crystallite is different and the magnetisation rapidly dephases. This can be envisaged pictorially from the chemical shift interaction. In the static powder pattern the frequency axis could be read as an orientation axis. Then in Figure 2.12 the two sets of spins starting off at A and B have different initial precession rates. The azimuthal phase angle picked up by each of these orientations after a time t is... 

When there is quadrupole splitting, two parameters are affected in pulse NMR compared to the situation without any splitting or the cw case. The first parameter is the precession rate around in the rotating frame which depends on both I and m where the transition is, say, between the levels m and m+1 and where m can have any value between -I and I. The precession rate in the presence of the quadru-... 

The effective precession rate of the magnetization around in the rotating frame during the rf irradiation is proportional to A. Thus, for example, the 7t/2 pulse length for the transition for 1=5/2 is 1/3 the length of a n/2 pulse for an equivalent -S. nucleus with the same y, or for that matter, for a 1=5/2 nucleus with the same y in the absence of a quadrupole splitting as in liquids. 

At p = p3, the system jumps to a new state of uniform precession of the director (UP2) with large reorientation (0 74 ) and slow precession rate. As displayed in Fig. 7, starting from the stable UP2 branch above pa and lowering the excitation intensity, one finds a large and rather complicated hysteretic cycle, which eventually flips back to the UPl solution at pg = 1.09. This part of the UP2 branch consists of alternatively stable and unstable regions exhibiting a series of saddle-node bifurcations. Eventually, this branch connects with the UPS one which makes a loop and connects with the UPl branch. 

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