The precessional motion

C. The Precessional Motion The proton appears to be behaving as spinning magnet and therefore, not only can it align itself with or oppose an external field, but also may move in a characteristic manner under the influence of the external magnet. 

To investigate multispin systems, the so-called electron spin transient nutation (ESTN) spectroscopy is recently elaborated. This is a version of pulsed ESR. Nutation is the precessional motion of spin. The method and its applications are detailed in the paper of Itoh et al. (1997). Chapters 1 and 8 describes that the determination of spin multiplicity becomes a very important problem in organic chemistry of ion-radicals. 

The precessional motion can be maintained by a suitable radio frequency field superimposed on the steady field. For example, in Fig. 9.38(b), when a steady field Hz is applied along the z axis and a radiofrequency field //,., is applied in the x-y plane and rotates in the same sense and at the same frequency as the precession, resonance occurs. Gyromagnetic resonance as outlined above is in principle the same as ferrimagnetic resonance referred to earlier (Section 9.3.1), except that in the former case the material is magnetically saturated by a strong applied field. In practice the steady field, which determines the Larmor frequency, is made up of the externally applied field, the demagnetizing field and the anisotropy field, and is termed the effective field He. Figure 9.39 shows the He values at which resonance occurs in some of the important communications and radar frequency bands. 

Derive an expression for the angular frequency of the precessional motion of an electron situated in a magnetic field. 

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... 

More recently, Gilbert (1955) [6,7] proposed an equation describing the dynamic behavior of M which incorporated the collision damping incurred by the precessional motion, in an effective damping field term. He assumed that the damping field is... 

The arrows indicate the possible transitions, i.e. give the positions of the lines in the Zeeman effect. Here the selection rules for the magnetic quantum number m must be taken into account. These can be deduced from the correspondence principle in exactly the same way as at p. 110 (see also Appendix XXI, (p. 308)). As m denotes the precessional motion about the direction of the field, the transition Am = +1 corresponds to the classical vibrations at right angles to H ... 

Theoretical value of rintra in the case of diffusion control Phase of the precessional motion Attenuation of the spin echo in PPG NMR experiments Larmor frequency... 

FIGURE 33.24 Illustration of the precessional motion of the magnetization vector. 

If /i is the dipole moment /xj of an atom, only the force component in the direction of the field will yield a net effect due to the precessional motion. 

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