Larmor precession frequency

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

When the anisotropy energy is large enough it prevents any precession of the magnetic moment of super-paramagnetic crystals. The magnetic fluctuations then arise from the jumps of the moment between different easy directions. The precession prohibition is introduced into the Freed equations in order to meet that requirement every time the electron Larmor precession frequency appears in the equations, it is set to zero 12). 

The radiofrequency, or frequency with which the spin vector rotates around the central axis Oz that induces a change in states, is called the Larmor precession frequency. The Irish physicist Larmor, whose work preceded NMR, has shown independently that to, the angular rotation frequency around a central axis Oz, has a value of ... 

Since the s orbitals do not have orbital magnetic moment, g — ge — 2.0023. A is an eneigy, which in SI units is expressed in joule. Sometimes it is convenient to have it expressed in frequency units, i.e. in hertz or in radians per second, and then we have to divide A by h or by h (ft = h/2n). In magnetic resonance there often is a factor 2jt which complicates life. The frequency which we refer to is the angular frequency or the Larmor precession frequency. Such frequency co is... 

Then, the electrons that surround each nucleus act to slightly perturb the magnetic held at the spin site. This causes the Larmor precession frequency to be modihed by the chemical environment of the spin. This effect, called the chemical shift, is described by the equation... 

The determination of the g factor thus requires a measurement of the Larmor and the cyclotron frequency. The electrons cyclotron frequency may conveniently be replaced by w /u> x w, where uj, is the ions cyclotron frequency. This is of advantage because the cyclotron frequency of the ion and the Larmor precession frequency can measured at the same particle. The ratio ujec/ujlc is the charge to mass ratio of the ion to the electron. For the case of Carbon it has been determined in Penning trap experiments by van Dyck and coworkers [16],... 

For a proton, the Larmor precession frequency g>n corresponds to 429 kHz gauss-1 (42.9 MHz T-1), which for a field of 14,000 gauss (1.4 T) corresponds to a frequency of 60 MHz. In analogy with Eq. (3.20.14), this external field B0 can also be associated with an external electric field Eq ... 

N, or 29Si. In CP, both nuclear spin species are spin locked and the rf amplitudes adjusted so that their Larmor precession frequencies in their respective rotating frames are equal the Hartmann-Hahn condition. The single-contact CP enhancement of the rare spins is given by yj/ys. Additional enhancement normally occurs because the CP experiment may be recycled at a rate limited by the usually much faster spin-lattice relaxation rate of protons rather than that of the rare spins. 

The third field region observed in the MARY curve shows a reversion of the field effect relative to the Zeeman effect saturation. We saw previously that the rate of S-Tq mixing depends on the difference in Larmor precession frequencies of the two radicals and that this difference may arise from a difference in the g-values of the radicals. This frequency difference is proportional to the strength of the applied field. As the g-value... 

Larmor precession frequency of iJ o)j = Larmor precession frequency of j... 

Fig. 22. General relationship between Tip value and correlation time (Vx is the Larmor precession frequency of H in a rotating frame. The shaded areas indicate hypothetical fragments with different molecular mobility. (Adapted with permission from Ref. 463.)...

For each field the precession frequency is proportional to the magnetic field the constant of proportion is y, the gyromagnetic ratio. For example, we have already seen that in the rotating frame the apparent Larmor precession frequency, 2, depends on the reduced field ... 

Here 1/Tj is the relaxation rate of the water nuclei in the protein-free buffer, V the Larmor precession frequency of the nuclei at field H, and D, A, and P are parameters that are determined by fitting Equation 2 to the data. Re stands for the real part of. ... 

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