Magnetic dipole interaction constant

Note that the magnetic dipole interaction constant a is a product of a nuclear quantity gj which is proportional to the moment, and an electronic quantity k which is proportional to the internal magnetic field strength. I and J process about their resultant F, as shown in Fig.2.15. We have... 

The magnetic dipole interaction constant a can frequently be determined accurately with precise methods which will be discussed in Chaps. 7 and 9. As we have mentioned, it represents a quantity in the field between atomic and nuclear physics. If the nuclear moment is known, the measurement yields an experimental value of the magnetic field at the nucleus which can be compared with the results of atomic calculations. If, on the other hand, the field can be calculated reliably, information on unknown nuclear moments can be obtained. The hyperfine structure will be particularly large if the atom contains an unpaired s electron, giving rise to the Fermi contact interaction, caused by the large probability of the s electron being foimd inside the nucleus. 

In analogy with the magnetic dipole interaction constant a the electric quadrupole interaction constant b is a product of a nuclear quantity Q, the electric quadrupole moment, and an electronic quantity qj, which is proportional to the electric field gradient. Thus, with the b factor experimentally determined, information on the nucleus or the electronic shell can be obtained. The electric hyperfine structure is of the same order of magnitude as the magnetic one, but generally somewhat smaller. It exhibits itself as a deviation from the Lande interval rule. In Fig.2.18 two examples of the combined action of magnetic and electric hyperfine structure are shown. 

In analogy with the magnetic dipole interaction constant a the electric qua-drupole interaction constant 6 is a product of a nuclear quantity Q, the electric... 

The magnetic-dipole interaction constants A of the 8 lowest levels have been measured by the ABMR method and compared to theoretical values, assuming that the off-diagonal hyperfine interactions were smaller than the experimental errors [4]. 

Furthermore, the works above have initiated several theoretical groups to calculate the electronic part of the magnetic dipole interaction [13, 81-84], obtained from the experimental dipole constant and gj-factor in "Fr (cL Eq. 2). The good agreement generally obtained for the magnetic hyperfine interaction indicate that the electronic wave functions obtained, reliably may be used in the evaluation of the spectroscopic quadrupole moments from the measured quadrupole constants. The value Q 2( "Fr) = -0.19 b, obtained from many-body calculations of the electronic pan of the hyperfine interaction [83], has been used as a reference value in the evaluation spectroscopic quadrupole moments. 

The electric quadrupole and magnetic dipole interactions both generate multiple-line spectra, and consequently can give a great deal of information. All three interactions can be expressed as the product of a nuclear term which is a constant for a given Mossbauer y-ray transition and an electronic term which can be varied and related to the chemistry of the resonant absorber being studied. 

One of the two or both nuclei of a diatomic molecule may interact with rotation via their electric quadrupole moments, or their magnetic dipole moments may interact with the rotational magnetic field. The two nuclei may be coupled by the direct (tensorial) or indirect (electron-coupled scalar) magnetic dipole interaction which also influences rotation. Furthermore, in a state other than E the nuclei cause magnetic perturbations when their dipole moments interact with those of the unpaired - electron spins or with the orbital magnetic field. The energetic effects of these so-called hyperfine interactions can be quantified with the aid of interaction constants which in favorable cases can be determined from high-resolution spectra. 

The connection between the rate constants W and molecular parameters is a complex subject that can only be outlined here. Basically, the dipole-dipole interaction is a through-space effect in which one nuclear magnetic dipole interacts with the local field created by a second nucleus. The value of W depends upon the component of this field that fluctuates at the frequency of the transition, that is at 0, (o and 2Larmor frequency. Working out the algebra shows that the cross-relaxation rates are proportional to spectral densities, which are Fourier transforms of time correlation functions that describe molecular motions ... 

Effective radial parameters of the magnetic dipole interaction for the 4d 5s configuration have been derived from the constants A [20] (in MHz) ... 

From experimental A values [2, 15, 28] the effective radial parameters (in MHz) of the magnetic dipole interaction have been derived, parameters being constrained to be equal to ab initio calculated values or to vary in the constant ratio of the spin-orbit constants [45] ... 

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