Combined Electric and Magnetic Hyperfine Interactions

Zeeman energies of the ground and the excited states, respectively. The splitting of the 7 = 3/2 state Into two dotted lines In the middle panel indicates the effect of quadrupole splitting discussed earlier 

The magnetic field contributions will be discussed in further detail in Chap. 5. 

Pure nuclear magnetic hyperfine interaction without electric quadrupole interaction is rarely encountered in chemical applications of the Mossbauer effect. Metallic iron is an exception. Quite frequently, a nuclear state is perturbed simultaneously by 

The monopole interaction 8 , which yields the isomer shift, is easy to treat it is just additive to all transition energies. Thus, the recorded spectrum has uniform shifts of all resonance hues with no change in their relative separations. 

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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...

Fig. 4.25. Schematic Mossbauer spectra to demonstrate how asymmetric line-widths can arise in a magnetic sextet spectrum. The independent effects of the electric quadrupole interaction and the magnetic dipolar contribution to the hyperfine field are shown separately in (u) and (h) respectively and these effects are summed in (c). An equally probable site has a combined electric quadrupole interaction and magnetic dipolar contribution to the hyperfine field of opposite sign and this spectrum is shown in (d). Sites with both signs of interaction are present in the material and therefore (c) and (d) are added to give the spectrum shown in (e). Finally the distribution in magnitude as well as sign of the interactions is included in the spectrum shown in (/) which models the actual conditions in a real solid. It is seen that the resulting spectrum has linewidths Fj where F, >F4, r2

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. 

Energy-level scheme and resultant spectra for the combined hyperfine interactions with a strong magnetic field. Part (a) represents the nuclear ground and excited states without hyperfine interactions, (b) with isomer shift, (c) the pure magnetic dipole splitting of ground and excited states, and (d) with additional line shifts due to first-order electric... 

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) ... 

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. 

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