Precession, nuclear moments

Figure 5.2 A pair of precessing nuclear moments (/i) with static (a) and rotating (b) components indicated. The second moment is at a distance r from the first, at an angle 6 with respect to the...

Figure 1.1. Nuclear precession nuclear charge and nuclear spin give rise to a magnetic moment of nuclei such as protons and carbon-13. The vector n of the magnetic moment precesses in a static magnetic field with the Larmor frequency vo about the direction of the magnetic flux density vector Bo...

Figure 4), but only those nuclear moments y with small values of h ( Hi) participate in the spin echo. (These are the moments y whose frequency of precession in the laboratory reference frame is near the rf frequency go.)... 

If only B0 is applied, the nuclear moments precess without any phase coherence. No resultant component of the magnetization in the x y plane is observed and M, equals M0 (Fig. 1.7(a)). 

As shown in Fig. 2.1 (b), the nuclear moments still precess with Larmor frequency v0 about the z axis in the xy plane, as does the resultant transverse magnetization (Figs. 2.1(b) and 2.2(b)). In the rotating frame (Section 1.7.3), the transverse magnetization with reference frequency v0 stands while faster or slower components with v( > v0 or v, < v0 will rotate clockwise or counterclockwise, respectively, as shown in Fig. 2.3. 

In c.w.-n.m.r. spectroscopy, a relatively weak, but rapidly oscillating, magnetic field is produced on the x axis by the application of a continuous, low-powered radiofrequency (r.f.) to the transmitter coil(s). As this radiofrequency approaches the resonance frequency, the magnetization vector is very slightly tipped out of the z axis, and precesses about this axis. When this frequency of precession is matched by the r.f. applied (the resonance condition), some of the individual, nuclear moments undergo transitions to the less-stable energy-level represented by precession about the — z direction, accompanied by absorption of energy from the transmitter coil. 

In general, the motion of M in the rotating frame follows from the classical torque exerted on it by Beff. The effect of an rf pulse is then to tip M away from the z axis and to generate a component in the x y plane. As viewed from the laboratory frame of reference, this component precesses in the xy plane and induces an electrical signal at frequency w in a coil placed in this plane. As the nuclear moments that make up M precess, they lose phase coherence as a result of interactions among them and magnetic field inhomogeneity effects, as described in Section 2.7. Thus Mxy decreases toward its equilibrium value of zero, and the... 

One might now ask how can precession of individual nuclear moments in the upper and lower quantum energy levels shown in Figure 4 permit continuous precession of the net macroscopic magnetization in the zy plane It is possible to obtain such... 

A second mode by which nuclear magnetic moments may interact is illustrated in Fig. 20.3. Here a pair of nuclear moments precess about the Bo-axis and each is decomposed into a static component along Bo (a) and a component rotating in the xy-plane (b) transverse to Bo. If the rotating component precesses at the Larmor frequency vq, then a... 

In paramagnetic solids, an important consideration arises from the fact that the correlation time Tq of the ionic spin fluctuations is shorter than the characteristic nuclear precession time t in the effective hyperfine field of (18.9). Thus, Tc < T, or Tc > ASIh. Under this condition, the nuclear moment senses only the average hyperfine field which is proportional to the average value of the spin. 

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