Zeeman lines

The level splitting and with it the frequency shift of the Zeeman line depends on the Lande g values in both levels. For the Ne line X = 3.39 u, for instance, this shift is 1.56 Mc/sec/Gaussfor the ruby line X = 6948 A it amounts to 3 Mc/Gauss, and a total shift of 5 cm has been obtained at 49 KGauss... 

Using a least squares iterative method, each spectrum is fitted with two Gaussian lines. The smooth curve seen on Fig. 2 corresponds to such a Gaussian fit. This procedure provides a rather accurate value of Fc, the frequency of the center of the two Zeeman lines. It provides also the Fc uncertainty interval. This interval is related to the difference between the best fit and the experimental spectrum, which is here mainly due to noise. 

Fig. 4. Excitation spectra of Pd(2-thpy)2 in n-octane (a) at T = 1.3 K and (b) to (e) at T=1.5 K, respectively. Concentration c = 10 mol 1 The emission is detected at v j t = 17,702 cm (18,418 cm - 716 cm vibrational satellite). The excitation spectra (b) to (e) show the region of the electronic origin near 18,418 cm on an enlarged scale. With application of high magnetic fields up to B = 12 T,the origin line at 18,418 cm (0-0 transition) splits into three Zeeman lines. (Compare Refs. [56,74])...

The appearance of more than six Zeeman lines indicates that the Zeeman... 

The results of thermal treatment of FeO to give Fe and Fe304 have been followed in the MSssbauer spectrum [23]. In some cases there was an apparent reduction in the quadrupole splitting of a sample which had been heated, and magnetic splitting appeared above the bulk FeO Curie temperature. The Zeeman lines were generally smeared out into a broad envelope. One possible explanation for this is that the microscopic variations in the site symmetry cause large variations in the orbital and dipolar contributions to the internal... 

The Zeeman line is now split with a quadrupolar splitting (Fig. 2.1) 3 e qQ... 

In practice, the emission line is split into three peaks by the magnetic field. The polariser is then used to isolate the central line which measures the absorption Ax, which also includes absorption of radiation by the analyte. The polariser is then rotated and the absorption of the background Aa is measured. The analyte absorption is given by An — Aa. A detailed discussion of the application of the Zeeman effect in atomic absorption is given in Ref. 51. 

The number of energy levels found to date, with the aid of the Zeeman effect and the isotope shift data, is 605 even and 586 odd levels for Pu I and 252 even and 746 odd for Pu II. The quantum number J has been determined for all these levels, the Lande g-factor for most of them, and the isotope shift for almost all of the Pu I levels and for half of those of Pu II. Over 31000 lines have been observed of which 52% have been classified as transitions between pairs of the above levels. These represent 23 distinct electron configurations. 

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

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... 

Fig. 4.10. The left side of the scheme represents the starting situation of pure Zeeman splitting, as described by (4.48) and shown before in Fig. 4.9. In this example, the field B = (0,0,B), which defines the quantization axis, is chosen as the z-direction. The additional quadrupole interaction, as shown on the right side of Fig. 4.10, leads to a pair-wise shift of the Zeeman states with mj = 3/2 and mi = 1/2 up- and down-wards in opposite sense. In first order, all lines are shifted by the same energy as expected from the m/-dependence of the electric...

The anisotropic/factor may also manifest itself in the relative line intensities of Zeeman split hyperfine spectra in a poly crystalline absorber. Expanding f(0) in a power series... 

In [49, 76], the line intensities for electric quadrupole and Zeeman (magnetic dipole) splitting and including the anisotropy of the /-factor are also given for / = 2 <-> 7g = 0 transitions (even-even isotopes, e.g., in the rare earth region or in W, Os). 

FIGURE 5.2 A schematic model of multiple X Y interactions. Black dots are unpaired electrons the central, big black dot is the point of EPR observation. Straight lines are interactions a single straight line symbolizes the electronic Zeeman interaction S B double lines represent central and ligand hyperfine interactions S I triple lines are zero-field interactions S S between electrons (i) around a single metal (ii) at different centers within a molecule and (iii) at centers in different molecules. 

Formally, this procedure is correct only for spectra that are linear in the frequency, that is, spectra whose line positions are caused by the Zeeman interaction only, and whose linewidths are caused by a distribution in the Zeeman interaction (in g-values) only. Such spectra do exist low-spin heme spectra (e.g., cytochrome c cf. Figure 5.4F) fall in this category. But there are many more spectra that also carry contributions from field-independent interactions such as hyperfine splittings. Our frequency-renormalization procedure will still be applicable, as long as two spectra do not differ too much in frequency. In practice, this means that they should at least be taken at frequencies in the same band. For a counter-example, in Figure 5.6 we plotted the X-band and Q-band spectra of cobalamin (dominated by hyperfine interactions) normalized to a single frequency. To construct difference spectra from these two arrays obviously will generate nonsensical results. 

---