Magnetization, time evolution

Fig. 7.17 Time evolution of the nuclear forward scattering for metallic Ni foil. All measurements except for the upper curve were performed with external magnetic field B = 4 T. The solid lines show the fit. The arrows emphasize stretching of the dynamical beat structure by the applied magnetic field. The data at times below 14.6 ns had to be rescaled (from [34])...

The essence of the DDIF method is to first establish a spin magnetization modulation that follows the spatial variation of the internal magnetic field within the individual pore. Such modulation is created by allowing spins to precess in the internal magnetic field. Then the diffusion-driven time-evolution (often decay) of such a modulation is monitored through a series of signal measurements at various evolution times tD. The time constant of this decay corresponds to the diffusion time of a molecule (or spin) across the pore and thus is a direct measure of the pore size. 

The techniques of u.SR and p-LCR are based on the fact that parity is violated in weak interactions. Consequently, when a positive muon is created from stationary pion decay its spin is directed opposite to its momentum. This makes it possible to form a beam of low energy (4 MeV) positive muons with nearly 100% spin polarization at high intensity particle accelerators such as TRIUMF in Canada, the PSI in Switzerland, LAMPF and BNL in the USA, KEK in Japan, and RAL in England. Furthermore the direction of position emission from muon decay is positively correlated with the muon spin polarization direction at the time of decay. This allows the time evolution of the muon spin polarization vector in a sample to be monitored with a sensitivity unparalleled in conventional magnetic resonance. For example, only about 101 7 muon decay events are necessary to obtain a reasonable signal. Another important point is that //.SR is conventionally done such that only one muon is in the sample at a time, and for p,LCR, even with the highest available incident muon rates, the 2.2 fis mean lifetime of the muon implies that only a few muons are present at a given time. Consequently, muonium centers are inherently isolated from one another. 

Fig. 3. Illustration of the origin of proton nuclear magnetic relaxation induced by a super-paramagnetic crystal. The water molecule (symbolized by a bee) experiences a magnetic field which fluctuates because of the translational diffusion and because of Neel relaxation. The bottom curve represents a typical time evolution of this field.

In FFC relaxometry, one is concerned with the time evolution of the parallel component M of the nuclear magnetization of a sample or, in more complex cases, of one or more of its constituents. The primary goal of the signal detection is to estimate M and not, like in NMR spectroscopy, to analyze the FIDs in any detail beyond a simple solid/liquid phase distinction. 

All the powerful methods of magnetic resonance, from solid-state nuclear magnetic resonance (NMR) to medical magnetic resonance imaging, depend on measuring the time evolution of a spin system following the application of one or more radio frequency pulses. In the visible and ultraviolet, ultrafast optical pulse sequences have been used for many years to measure both population dynamics and coherence phenomena. At low... 

In our introduction to the physics of NMR in Chapter 2, we noted that there are several levels of theory that can be used to explain the phenomena. Thus far we have relied on (1) a quantum mechanical treatment that is restricted to transitions between stationary states, hence cannot deal with the coherent time evolution of a spin system, and (2) a picture of moving magnetization vectors that is rooted in quantum mechanics but cannot deal with many of the subder aspects of quantum behavior. Now we take up the more powerful formalisms of the density matrix and product operators (as described very briefly in Section 2.2), which can readily account for coherent time-dependent aspects of NMR without sacrificing the quantum features. 

Thus, the precise time evolution of the population of the various hyperhne states can be calculated for any given magnetic held. For the determination of MFEs, the singlet or triplet character of the pair is readily calculated, for example, using the singlet projection operator. 

Fig, 8. Time evolution of the spin-polarized EPR signal of prereduced RCs (P I Q ) treated as in Fig. 7. Note the inversion of the 3 ms spectrum with respect to the unpolarized 40 ms spectrum. The shoulder at low g value in the 50 /its spectrum is due to magnetic interaction with P. From Ref. 128. 

Fig. 6-8. Time evolution of the pyrene anion (A ) and triplet pyrene ( A ) of the reaction (6-21) in methanol measured in the absence and presence of a magnetic field of 50 mT. For each wavelength and magnetic field, 8-10 transients were averaged with a transient digitizer (time resolution 0.5 ns). (Reproduced from Ref. [23b] by permission from The American Institute of Physics)...

In the case of the stimulated spin echo, the tt rf pulse is replaced by two 7t/2 rf pulses that are separated by a magnetization-storage period during which migration occurs. We can write the time evolution operator for the sequence as... 

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