Magnetic Dipole and Electric Quadrupole Interaction

Steiner et al. have measured the magnetic hyperfine field of and in iron 

Chemical information from hafnium Mossbauer spectroscopy can primarily be deduced from the quadrupole-splitting parameter. In Table 7.4, we have listed the quadrupole coupling constants eQV for some hafnium compounds. Schafer et al. 

Nuclear resonance absorption for the 136 keV transition has been established by Steiner et al. [174]. The authors used a metal source and an absorber of metallic tantalum to determine the mean lifetime of the 136 keV level from the experimental line width ( 52.5 mm s for zero effective absorber thickness) and found a value of 55 ps. This has been the only report so far on the use of the 136 keV excited state of Ta for Mossbauer experiments. 

2 keV excited state of Ta appears to be most favorable for Mossbauer spectroscopy from the point of view of its nuclear properties  

The small natural width of 2E = 0.0065 mm s implies an extremely narrow relative line width of r/ y = 1.1 lO, which is about 30 times narrower than that for the 14.4 keV state of Fe. 

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The low-temperature Mossbauer spectra of the spinel type oxides, NiCr204 [14,18] (Fig. 7.6b) and NiFe204 [3, 18], have been found to exhibit combined magnetic dipole and electric quadrupole interaction (Fig. 7.7). For the evaluation of these spectra, the authors have assumed a small quadrupolar perturbation and a large magnetic interaction, as depicted in Fig. 7.3 and represented by the Hamiltonian [3]... 

MS2 Study of magnetic dipole and electric quadrupole interactions, two Ni sites differing in angle between H and EFG axis phase transitions in NiS2.oo NiS 1 96... 

The quantities A and B are usually called the constants of the magnetic dipole and electric quadrupole interactions. The nuclear matrix elements in (22.27) for k = 1 and 2 are proportional to the magnetic dipole p and electric quadrupole Q nuclear momenta, respectively ... 

In part the interest arises from the fact that the spectroscopic state 87/2 is the same for the atom, 4f 6s as for the divalent ion, 4f . The former has been studied by atomic beam triple resonance (Sandars and Woodgate 1960, Evans et al. 1965), and the latter by ENDOR (Baker and Williams 1962) in Cap2, an environment with cubic symmetry. For a half-filled shell, with no orbital momentum and a spherical distribution of electron spin moment with zero density at the nucleus, both the magnetic dipole and electric quadrupole interactions should be zero. Experimentally, they are small compared with the values for other odd-proton lanthanide isotopes with comparable nuclear moments, for which the hyperfine... 

The determination of peak intensities becomes a more complicated issue in the case of combined hyperfine magnetic dipole and electric quadrupole interactions (for the case of Fe see, e.g., Kundig (1967) and Housley et al. (1969)), or when the Mossbauer transition has a mixed (most often Ml + E2) multipole character (for the case of Ru see, e.g., Foyt et al. (1975)). Further factors influencing the relative peak intensities will be discussed in O Sect. 25.2.7.5. 

An example of a more recent experiment is the study of hyperfine structure of highly excited levels of neutral copper atoms, which yielded the magnetic-dipole and electric-quadrupole interaction constants. The experimental results allowed a comparison with theoretical calculations based on multiconfiguration Hartree-Fock methods [12.26]. Measurements of lifetimes [12.27] and of state multipoles using level-crossing techniques can be found in [12.28]. 

Combined magnetic dipole and electric quadrupole interaction... 

Often all three interactions, i.e. the electric monopole, magnetic dipole and electric quadrupole interactions, occur simultaneously. If the quadrupole interaction is small compared with the magnetic interaction (Eq j[i )> a correction to the interaction energy may be applied using first-order perturbation... 

The expressions given above provide the theoretical formalism for the description of all forms of polarized Raman scattering through first-order in the magnetic dipole and electric quadrupole interaction of light with matter. This is sufficient to describe the various forms of ROA within the assumptions given above. 

The hyperfine interaction constants A and B had been derived from ABMR measurements for the first four levels of the ground quintet [1]. Combining this method with the triple resonance technique, Biittgenbach et al. have obtained more precise values of the constants for p5 and [6]. These constants, corrected by use of the intermediate-coupling wave functions developed by Trees [7] are given in Table 2/1. From the constants A and B effective radial parameters of magnetic dipole and electric quadrupole interaction for the 4d 5s configuration have been derived [6, 16] (in MHz) ... 

Effective radial parameters of the magnetic dipole and electric quadrupole interaction for the 4d 5s configuration have been derived [40] (in MHz) ... 

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