Hyperfine Anomaly

An interesting effect, called hyperfine anomaly, has been observed by Wagner and Zahn [268] and by Perlow et al. [275] for the 73 keV transition of Ir, which apparently has favorable characteristics to establish this phenomenon. 

After four decades, the study of hyperfine anomalies may see a revival ... 

The evaluation of the magnetic dipole moments from the measured A-factors is generally made through a direct comparison with a stable isotope in which the values of I, p. and A are known. Neglecting the hyperfine anomaly (cf. below), the following relation holds within a given level of an element ... 

Here, I will not discuss the hyperfine anomaly nor the additional important nuclear information on changes of mean square charge radii obtained from isotope shift (IS) data in optical experiments. 

In an effort to determine differential hyperfine anomalies (Eq. 4) by high-precision measurements of dipole constants and nuclear g-factors, the two atomic-beam groups above have installed an upgraded atomic-beam apparatus at ISOLDE [32]. 

Metal ENDOR. ENDOR spectra from the central ions Cu, Ag and Ag have been recorded for Bq in the porphyrin plane (Table 6.1). In both compounds the metal hfs tensors are axially symmetric within experimental error. The ratio of the Ai values of the two Ag isotopes, Ai( Ag)/Ai( Ag) = 0.8664 0.0002, is significantly smaller than the ratio of the two nuclear g-factors gn( Ag)/gn( ° Ag) = 0.8698. This difference arises from the penetration of unpaired s-electron density into the nuclei ° Ag and Ag which have different nuclear charge distributions (hyperfine anomaly )). 

Effects on the hyperfine constants are relatively smaller in magnitude. For the magnetic hfs, the correction in the parallel direction is only 0.1%, but zero for the perpendicular direction. The latter was therefore used to obtain the best ratio for the two isotopes 147/149 of the magnetic hyperfine constants. The result, 1.21337(3), is more accurate than the atomic beam result 1.2130(3), but the close agreement indicates that any hyperfine anomaly is very small, as would be expected from the fact that the magnetic hfs comes overwhelmingly from the 4f electrons. On this basis, the ratio of the magnetic hyperfine constants should be equal to that of the nuclear moments. 

The nuclear moments p,i and Qs can be extracted from A and B using empirical or theoretical values for the magnetic hyperfine field HdO) and the electric field gradient factor measurements (g = iii/.IfiM) on the stable isotopes. semi-empirical or theoretical analyses, unless precise values are available from the hfs of muonic atoms. 

This relation is b ed on the assumption that the k value is the same for both isotopes. Since fe, to a first approximation, is only related to the electronic shell, such an assumption is very reasonable. However, small differences in k can occur due to electron penetration into the nucleus (s-electrons). This results m a deviation from the relation in (7.21), or a so-caJled hyperfine anomaly [7.9]. However, tliis anomaly is generally less than 1%. The dipole moment of the nucier can also be determined dir ectly by high-precision ABMR measurement in high magnetic fields, by observing the small direct contribution from the nucleus. 

M.G.H, Gustavsson, A.-M, Martensson-Peildrill Four decades of hyperfine anomaly. Adv. Quantum Chem, 30, 343 (1998)... 

Clark, M.E. Cage, G.W. Greenlees, The hyperfine structure and hyperfine anomaly of Dy and Dy, Phys. Lett. 62A 439... 

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