Magnetic dipole resonance

Energy dependence of the functions Fm in the case of nuclear resonant scattering from a magnetic dipole resonance between nuclear spins lg= /2 and 4 = 3/2. 

It is much more difficult to observe the Mossbauer effect with the 130 keV transition than with the 99 keV transition because of the relatively high transition energy and the low transition probability of 130 keV transition, and thus the small cross section for resonance absorption. Therefore, most of the Mossbauer work with Pt, published so far, has been performed using the 99 keV transition. Unfortunately, its line width is about five times larger than that of the 130 keV transition, and hyperfine interactions in most cases are poorly resolved. However, isomer shifts in the order of one-tenth of the line width and magnetic dipole interaction, which manifests itself only in line broadening, may be extracted reliably from Pt (99 keV) spectra. 

We have learned from the preceding chapters that the chemical and physical state of a Mossbauer atom in any kind of solid material can be characterized by way of the hyperfine interactions which manifest themselves in the Mossbauer spectrum by the isomer shift and, where relevant, electric quadrupole and/or magnetic dipole splitting of the resonance lines. On the basis of all the parameters obtainable from a Mossbauer spectrum, it is, in most cases, possible to identify unambiguously one or more chemical species of a given Mossbauer atom occurring in the same material. This - usually called phase analysis by Mossbauer spectroscopy - is nondestructive and widely used in various kinds of physicochemical smdies, for example, the studies of... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

Modem structural chemistry differs from classical structural chemistry with respect to the detailed picture of molecules and crystals that it presents. By various physical methods, including the study of the structure of crystals by the diffraction of x-rays and of gas molecules by the diffraction of electron waves, the measurement of electric and magnetic dipole moments, the interpretation of band spectra, Raman spectra, microwave spectra, and nuclear magnetic resonance spectra, and the determination of entropy values, a great amount of information has been obtained about the atomic configurations of molecules and crystals and even their electronic structures a discussion of valence and the chemical bond now must take into account this information as well as the facts of chemistry. 

In the remainder of this section, we will consider only electric-dipole transitions. These are the strongest transitions, and account for most of the observed atomic and molecular spectroscopic transitions. (Magnetic-dipole transitions occur in magnetic-resonance spectroscopy.) When the integral d vanishes, we say that a transition between states n and m is forbidden. 

The earliest work employed the method of moments, and Fraissard et al (192) were the first to consider in detail the second moment of the proton NMR resonance in nonspinning solids. In general, when the line shape is determined solely by the I-I and I-S magnetic dipole-dipole interaction, the Van Vleck second moment, M2, is given by (193)... 

The presence of a magnetic dipole moment in many nuclei that have an intrinsic spin has found enormous application in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). NMR is extensively used in chemical laboratories to identify the structural and chemical environments of the nuclei in molecules, whereas MRI uses a tomographic technique to locate specific molecules... 

Measuring the M intervals by microwave resonance techniques generally yields the fine structure intervals as well. However, A = 0 transitions between the fine structure levels can also be examined by several other techniques. The first of these is rf resonance. Since the transition involves no change in Z it is not an electric dipole transition but rather a magnetic dipole transition, and a straightforward approach is magnetic resonance, which has been used by Farley and Gupta36 to measure the 6f and 7f fine structure intervals in Rb. Their approach is... 

While the fine structure transitions are inherently magnetic dipole transitions, it is in fact easier to take advantage of the large A = 1 electric dipole matrix elements and drive the transitions by the electric resonance technique, commonly used to study transitions in polar molecules.37 In the presence of a small static field of 1 V/cm in the z direction the Na ndy fine structure states acquire a small amount of nf character, and it is possible to drive electric dipole transitions between them at a Rabi frequency of 1 MHz with an additional rf field of 1 V/cm. 

Spin does not appear in the Schrodinger treatment, and essentially has to be postulated. There are more sophisticated versions of quantum theory where electron spin appears naturally, and where the magnetic dipole appears with the correct magnitude. I want to spend time discussing electron spin in more detail, before moving to the topic of electron spin resonance. 

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