Linear precession

As with any other homonuclear decoupling, the transverse magnetization of the 13C , for example in the evolution time, is perturbed by the decoupling pulse, resulting in an additional precession virtually around the z axis. Since the adiabatic decoupling is applied during the entire evolution time of the 13C , a non-linear frequency shift rather than a phase shift appears in the spectrum. This is termed the Bloch-Siegert (frequency) shift in the NMR literature in honour of their discovery of the phenomenon. 

In this chapter, dielectric response of only isotropic medium is considered. However, in a local-order scale, such a medium is actually anisotropic. The anisotropy is characterized by a local axially symmetric potential. Spatial motion of a dipole in such a potential can be represented as a superposition of oscillations (librations) in a symmetry-axis plane and of a dipole s precession about this axis. In our theory this anisotropy is revealed as follows. The spectral function presents a linear combination of the transverse (K ) and the longitudinal (K ) spectral functions, which are found, respectively, for the parallel and the transverse orientations of the potential symmetry axis with... 

In the framework of the standard linear response theory, the relaxation times of precession are determined in the a< 1 limit according to the generic formula x = (ay//)-1. Setting the field equal to its resonance value, we get... 

Figure 12 Population transfer during precession (D) and exchanges (X) at the rth exchange. The population of basis coherences (see spots on lines) is transferred to eigencoherences (and vice versa) based on the linear combination of coefficients (spots on arrows). Colours black and grey have no meaning apart from making the alterations in the population of coherences visible.

We thus see that the purely magnetic evolution (4.11) of the polarization moment is, in essence, a linear change in time of its phase ip according to (4.12), with conservation of the module Mod pq (circle in Fig. 4.1(c)). The factor e1 means that the dependence pq (t) is periodic with a period Tq = 2ir/Qu)ji, i.e. that each transversal component of a polarization moment passes into itself with its own frequency Quj>. This is in full agreement with what has been said before in Section 2.3 on the connection between the coherence and symmetry of p(6,ip). The model presented affords the conservation of the shape of the angular momenta distribution p(0,ip) in the course of precession (see Fig. 4.1(6)). Incidentally, it may not seem quite appropriate in this context to maintain the statement that the magnetic field itself destroys coherency , as described by the transversal components pq, Q 0. Indeed, it follows from (4.11) that at... 

Fig. 4.18. Top diagrams - changes in time ( pulsations ) of the angular momenta probability density pb(9,

A vitally important aspect of ion trap operation is the ability to impart translational energy selectively to ions via resonance absorption of alternating current (ac) voltages (10-450 kHz) applied to the endcap. Unlike for linear quadrupole (or other multipole) collision cells, the absorption of energy is m/z specific as each m/z in the trap precesses at a specific set of frequencies, the most important of which for MS/MS is ooz, the fundamental frequency of motion in the z dimension, which is defined by... 

Figure 19. Measured linear variation of the resonance frequency, corresponding to absorption maxima, on the applied magnetic field. The slope gives g = 2.02. Inset similar variation obtained for the quality factor G = BJai representing a lower bound of the coherence time of molecular spin precession.

In this book, we adopt a form in which the function is expressed as a linear combination of spherical harmonics. This form is particularly appropriate for systems with near-spherical symmetry (such as Rydberg states or molecules which conform to Van Vleck s pure precession hypothesis [68, 69]) and is also consistent with the spirit of spherical tensors, which have the same transformation properties under rotations as spherical harmonics. The functional form of the ket rj, A) is written... 

The precessional motion of the magnetic moment around Bq occurs with angular frequency wq, called the Larmorfrequency, whose units are radians per second (rad s ). As Bq increases, so does the angular frequency that is, coq cx Bq, as is demonstrated in Appendix 1. The constant of proportionality between o>o and Bq is the gyromagnetic ratio 7, so that wq = Bq. The natural precession frequency can be expressed as linear frequency in Planck s relationship AE = Hvq or angular frequency in Planck s relationship AE = h(x)Q (coq = 2 rrvo). In this way, the energy difference between the spin states is related to the Larmor frequency by the formula... 

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