Magnetic hyperfine structure

Associated with its spin angular momentum I, a nucleus has a magnetic dipole moment /ij 

In this expression, which is analogous to (2.9,23,24), the nuclear magneton /Xn = Mb/8i (Si ) is a constant of proportionality. At the site of the nucleus the electron shell exhibits an effective magnetic field Bj directed along the atomic axis of rotation J, i.e.. 

There will be a magnetic coupling (orientational energy) between the nucleus and the electron shell and the interaction is described by 

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 energy contribution is calculated from (2.38) in the same way as the spin-orbit interaction (2.15) 

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A detailed study of the magnetic hyperfine structure in Mossbauer spectra and the performance of DFT methods is available [25]. It is known that DFT typically... 

Magnetic Hyperfine Structure. The magnetic fields in most magnetic iodine and tellurium compounds are not sufficient to separate the 18 magnetic hyperfine lines of the two iodine isotopes. Several measurements (13, 21, 34, 36) have indicated that fields of only about 100 kilo-gauss can be expected from such compounds. Therefore, other methods must be utilized. 

In our laboratory, we spend much of our time identifying contaminants. The studies described here are a case in point. Thus, the majority of the iron in the two samples described above belongs to a spectral component, NP (for nanoparticles), that exhibits magnetic hyperfine structure at 4.2 K. In whole cells, this component undoubtedly originates from ferric nanoparticles. What is the spectroscopic basis of this statement NP exhibits at 120 K a quadrupole doublet with AEQ = 0.65 mm/s and 5 = 0.45 mm/s. 

Miller and Townes [122] studied the magnetic hyperfine structure arising from the 170 nucleus in the 160170 isotopomer and were able to obtain information about the magnetic hyperfine parameters. We do not go into the details here, but will discuss... 

Table 4.3 Magnetic Fields Derived from Magnetic Hyperfine Structure (41)...

Influence of iron concentration. Spectra have also been recorded for a sample exchanged with Mohr s salt, neutralized to about 60 % and containing 17 % water. Hyperfine parameters are identical to those obtained for the less neutralized samples exchanged with ferrous chloride. There is no evidence in spectra at 4.2 K for magnetic hyperfine structure at this neutralization level and the lack of any significant magnetic interactions is also evident from the susceptibility which follows a simple Curie law down to 4.2 K. It follows that the ferrous ions are physically isolated from each other over a wide range of iron concentration. 

Cs impurity atoms in an iron foil have been studied by implantation from Xe atoms which / -decay to caesium [128]. Partially resolved magnetic hyperfine structure is seen, giving a value for the field at the Cs nucleus of +273(10) kG. 

PPyFePcTs. This would be expected if the Fe(Ill) nuclei within PPyFePcTs were closely associated, suggesting a structure in which the majority of the counter-anions are aggregated. The absence of magnetic hyperfine structure at 4.2 K appears to contradict the EPR data which showed evidence of a magnetic interaction between the polymer radicals and para-... 

Leung et al. [06Leu] have measured electronic ground state rotational transitions and their nuclear electric quadrupole and magnetic hyperfine structures in the n = 0 and o = 1 vibrational states using MWFT spectroscopy. From the vibrational dependence of the fitted spectroscopic parameters their equilibrium values could be determined. 

The ratios of the quadrupole splitting for the two isotopes 151/153 are 0.3857(2), but a small correction for second-order effects of the magnetic hyperfine structure increases the ratio to 0.3900(8). This is slightly higher than the ratio of 0.3874(3) found by Erickson and Sharma (1981) from measurements on Eu " in YAIO3, but bisects the two ratios of the quadrupole constants B listed in table 3. 

Isotope effects in atoms are on the order of p 10 and the magnetic hyperfine structure scales roughly as a pZgnuc 10 Zgnuc, where gnnc is the nuclear g-factor. One has to keep in mind that g uc also depends on p and the quark parameters Xq. This dependence has to be considered when comparing, for example, the frequency of the hyperfine transition in Cs (Cs frequency standard) [5] or the hydrogen 21 cm hyperfine line [30,31] with various optical transitions [5]. 

Frosch, R.A., Foley, H.M. Magnetic Hyperfine Structure in Diatomic Molecules. Phys. Rev. 88 (1952) 1337. 

As for the fine stucture, the Lande interval rule is also valid for the magnetic hyperfine structure... 

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