Larmor speed

A nuclear electric quadrupole moment arises from a non-spherical distribution of electrical charges in the nucleus. Because the energy of an electric quadrupole moment depends on its orientation with respect to an EFG, a randomly varying electric field gradient associated, for example, with molecular rotation having a finite amplitude of its spectral density at the Larmor speed can induce effective relaxation of the quad-rupolar nucleus. In liquids, it is possible to write down... 

While Tp the Zeeman relaxation time, is sensitive to motions occurring at the Larmor speed in the large applied field, the dipolar relaxation time is sensitive to fluctuations occurring at the Larmor speed in the local field which is three to five orders of magnitude smaller. The former might be in the range of 5-300 MHz while the latter will be in the few kHz range. 

Figure 2.16. Effect of a changing distribution in the main component of the electric field gradientVzz comparing the effect on A. the satellite transition and B. the centreband with a mean quadrupole frequency of 1 MHz and then a distribution of quadrupole frequencies as shown. Only one half of the satellite transition is shown. The Larmor frequency is 104.26 MHz and a spinning speed of 11.5 kHz has been taken. From Jager et al. 1993 with permission of the copyright owner.

Figure 3.18. The dependence of the intensity of the centreband of an MAS spectrum for the A. central and B. satellite transition as a function of the spinning speed v, the quadrupole frequency vq and the Larmor frequency Vo along with C. the Al MAS NMR spectrum of Y3AI5O12 at 7.05 T at a spinning speed of 7 kHz. From Massiot et al. (1990) with permission of copyright owner.

In a SR source the electron moves at a speed close to c so that for a radius of curvature, q, the relativistic generalisation of the Larmor formula is... 

Solid-state Al NMR spectra were recorded at 9.4 T on a Bruker Avance400 spectrometer at 14 kHz spinning speed. Simple one-pulse sequences with phase cycling were used. The Larmor fiequency was 104.26 MHz, the pulse length... 

When an electron is accelerated, it produces electromagnetic radiation. The power radiated by an accelerated charge, P, whose speed is significantly less than the speed of light, is described in classical electrodynamics by the Larmor formula. In a synchrotron, the electrons are moving at a speed close to the speed of light (relativistic electrons). The power radiated by relativistic electrons is given by... 

Fig. 18. 35 GHz cw ENDOR signal from O (/ = f) of nitrile hydratase in 35% enriched H2 0, taken at the high-held edge ( 3) of the EPR envelope. The quintet shown represents the v+ branch of the 0 ENDOR pattern that is centered at the O Larmor frequency, 7.3 MHz (filled triangle). The quadrupole splittings and hyperfine values calculated are estimated using second-order perturbation theory in the nuclear quadrupole interaction for an O nucleus. Conditions 12,650 G, 34.92 GHz, 0.16 mW microwave power, 1 G modulation amplitude, 0.5 MHz/sec if scan speed, 2 K. (Adapted from Jin et al. )...

As the rate of rotation increases, the rotational spinning sidebands move further out and become weaker. At very high spinning speeds, the intensities of the sidebands become negligible, and the spectrum consists of the narrowed central line at the Larmor frequency, coq. The intensities of the first satellites are expected to decrease at a rate of a>, thus preserving their contributions to the second moment of the entire spectrum. Indeed, the magnirnde of the second moment of the spectrum should be invariant with respect to rotation. The intensities of the second and higher satellites fall even more rapidly with an increase in cur, as cu " for the nth satellite. 

---