Interaction magnetic dipole

A nucleus in a state with spin quantum number 7 > 0 will interact with a magnetic field by means of its magnetic dipole moment p. This magnetic dipole interaction or nuclear Zeeman effect may be described by the Hamiltonian... 

Magnetic dipole interaction Hm (4.47) and electric quadmpole interaction //q (4.29) both depend on the magnetic quantum numbers of the nuclear spin. Therefore, their combined Hamiltonian may be difficult to evaluate. There are closed-form solutions of the problem [64], but relatively simple expressions exist only for a few special cases [65]. In Sect. 4.5.1 it will be shown which kind of information can be obtained from a perturbation treatment if one interaction of the two is much weaker than the other and will be shown below. In general, however, if the interactions are of the same order of magnitude, eQV Jl, and... 

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

Spin-spin relaxation is primarily induced by magnetic dipole interactions between paramagnetic ions. Usually, the most important spin-spin relaxation process is the so-called cross-relaxation process in which a transition of an ion / from the state K) to toe state is accompanied by a transition of another ion j from the... 

Fig. 7.3 Effect of magnetic dipole interaction (7/m), electric quadmpole interaction (Hq), and combined interaction// = Hu + //q, Em> q on the Mossbauernuclear levels of Ni. The larger spacings between the sublevels of the ground state are due to the somewhat larger magnetic dipole moment of the nuclear ground state as compared to the excited state. The relative transition probabilities for a powder sample as well as the relative positions of the transition lines are indicated by the stick spectra below...

In experiments with magnetic fields between 13 and 55 mT (130-550 G) applied to the single crystal source, the authors of [58] observed magnetic dipole interaction in addition to electric quadmpole splitting in a reduced spectrum (Fig. 7.22) [58]. They determined the magnetic moment of the excited 1/2 state to be U(l/2 ) = +(0.58 0.03))In-... 

Apart from the determination of nuclear parameters, the Mossbauer transition in Os, especially the 36.2 and 69.6 keV transitions, are suited for chemical applications. As shown below, the 36.2 keV level, in spite of its large half-width, can be well used for the measurement of isomer shifts, whereas the 69.2 keV state is favorable for the characterization of electric quadrupole or magnetic dipole interactions. Both Mossbauer levels are populated equally well by the parent isotope lr, and simultaneous measurement is possible by appropriate geometrical arrangement. 

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. 

The physical interpretation of the anisotropic principal values is based on the classical magnetic dipole interaction between the electron and nuclear spin angular momenta, and depends on the electron-nuclear distance, rn. Assuming that both spins can be described as point dipoles, the interaction energy is given by Equation (8), where 6 is the angle between the external magnetic field and the direction of rn. 

Nuclear Overhauser effect—The nuclear Overhauser effect (NOE) occurs only between nuclei that share a dipole coupling, i.e., their nuclei are so close that their magnetic dipoles interact. Techniques that use NOE enhance spectra and allow spacial relationships of protons to be determined. 

Fig. 7.4 Top Nuclear energy levels of Fe as shifted by electrical monopole (left), or as split by electrical quadrupole (center) or by magnetic dipole interaction (right), schematized for hematite at room temperature (5 > 0 vs. a-Fe, EQ < 0, Bhf 0). Bottom Schematic Mossbauer spectra corresponding to the energy levels schematized on top (J. FriedI, unpubl.).

Liquids. In liquid solutions the concentration of transition ions can be kept small enough so that magnetic dipole interactions and exchange... 

This term is called the Fermi contact term. That part of the electron-nucleus magnetic-dipole interaction represented by (8.104) depends on the angular coordinates of the electron and is therefore anisotropic in contrast, the Fermi contact energy (8.108) is isotropic. The contact term plays an important role in the electron-coupled nuclear spin-spin interactions seen in the NMR spectra of liquids. 

Magnetic dipole interactions are possible for the 1AJ -3S ," and 129+ <-3E9 transitions in 02, although naturally they are weak. The transitions are, however, known both in absorption, especially in the atmosphere, and in emission indeed, the two band systems are frequently known as the infrared atmospheric and atmospheric bands of oxygen, and the observation of emission from these systems has often been used to demonstrate the presence of excited singlet oxygen both in the laboratory and in the atmosphere. 

Another mechanism of relaxation is associated with the magnetic interaction between nuclei and paramagnetic electrons (the so-called magnetic dipole interactions). This process is known as spin-spin relaxation time (T2). 

That is pa (Hp) is the wavefunction of G in the presence of a uniform external magnetic field, Hp, approximating the perturbation by the linear magnetic dipole interaction H (Hp). The rotational strength of the fundamental excitation of mode i is then... 

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