Zeeman pattern for

In order to assign the Zeeman patterns for the three lowest rotational levels quantitatively, one must determine the spacings between the rotational levels, and the values of g/and gr-In the simplest model which neglects centrifugal distortion, the rotation spacings are simply B0. /(./ + 1) this approximation was used by Brown and Uehara [10], who used the rotational constant B0 = 21295 MHz obtained by Saito [12] from pure microwave rotational spectroscopy (see later in the next chapter). The values of the g-factors were found to be g L = 0.999 82, gr = —(1.35) x 10-4. Note that because of the off-diagonal matrix elements (9.6), the Zeeman matrices (one for each value of Mj) are actually infinite in size and must be truncated at some point to achieve the desired level of accuracy. In subsequent work Miller [14] observed the spectrum of A33 SO in natural abundance 33 S has a nuclear spin of 3/2 and from the hyperfine structure Miller was able to determine the magnetic hyperfine constant a (see below for the definition of this constant). 

In the ADAS data bank [23,24] one can find further spectral transitions. The so-called X-Paschen program, which was brought in as module 603, allows us to display the Zeeman pattern for a variety of elements like Bn, Bei-m, Ci-V, Hel, Ol, Krl, Mgn, Nai, Cai-ll, Nel-ll, Sii-iv, and 60 lines from 115nm to 910 nm. The variation of the pattern can be studied for different T[, B, field direction, observation angle, and apparatus function. 

Figure 4. Zeeman patterns for two lines of U I The no-field lines are shown in the middle...

Fig. III.19. Calculated Zeeman spectra of the 2n—22o rotational transition show how the correct set of rotational g -values may be deduced from the Zeeman splittings at intermediate fields where the off-diagonal quadrupole hyperfine matrix elements cause different mixing of states and thus different Zeeman patterns for the two choices. (The observed spectra corresponds to the pattern on the left with g a negative). The calculated patterns were obtained by numerical diagonalization assuming Lorentzian lineshapes with half-widths of 40 kHz for the satellites...

Figure 6.15 Calculated Zeeman patterns for the perturbed rotational levels of CN A2If (v = 10) B2 + (v = 0). Only the 2II A-doublet and 0-components involved in the perturbation are shown. The horizontal axis is labeled in units of /ro(4.6688 x 10-5 cm 1/G) multiplied by the magnetic field (H) to give reciprocal centimeters rather than Gauss. [FVom Radford and Broida (1962).]... 

From (4.56) and Table 4.3, we derive the relative intensity ratios 3 2 1 1 2 3 for the hyperfine components of a Zeeman pattern of a powder sample. The transition probability for the case of the polar angle 6 = Oq can readly be calculated by integrating (4.56) only over the azimuthal angle (j). One obtains a factor (1 + cos 0o)/2 and sin 0o for m = 1 and m = 0, respectively, which are multiplied by the square of the Clebsch-Gordan coefficients. As a consequence of the angular correlation of the transition probabilities the second and fifth hyperfine components (Fig. 4.17) disappear if the direction k of the y-rays and the magnetic field H are parallel (0q = 0). 

The Zeeman effect of arsenic spectra has been studied,1 and wavelengths, classifications and Zeeman patterns have been determined for 11 lines in As I, 64 lines in As II and 2 lines in As III. 

Figure 35. (a) Zeeman-splitting pattern for the one-electron band levels of ZnO DMSs with H z. 

Fig. 5.2. Zeeman energy level pattern for the OD A2T,+, v = 0, IV = 1, J = 3/2 level as a function of magnetic field.

Figure 10.73. Observed Zeeman pattern and theoretical reconstruction for a J = 3/2 —> 3/2 transition in HeAr+, with a rest frequency of 35 092.7 MHz [211]. The magnetic field was 4.85 G, using the TE10 mode with parallel ion beam and microwave propagation, but perpendicular microwave electric field and static magnetic field (AM/ = 1).

The second diagnostic study made use of the Zeeman effect, observed when a small magnetic field was applied parallel to the ion beam direction. For almost every line in the spectrum a Zeeman splitting could be observed figure 10.73 illustrates a particularly simple example, where the six-line Zeeman pattern shows conclusively that the resonance must arise from a J = 3/2 3/2 transition. Effective g factors... 

In the microwave ion beam experiments described in this section, it is important to identify the microwave mode corresponding to the resonance line studied in a magnetic field. For a TM mode the microwave electric field along the central axis of the waveguide is parallel to the static magnetic field. We then put p = 0 in equation (10.161) so that the Zeeman components obey the selection rule AMj = 0. Alternatively in a TE mode the microwave electric field is perpendicular to the static magnetic field and the selection rule is A Mj = 1. This is the case for the Zeeman pattern shown in figure 10.73 each J = 3/2 level splits into four Mj components and the six allowed transitions should,... 

The value of K was obtained either from spectra of a series of samples having known average particle sizes at constant temperature or from spectra recorded as a function of temperature of a sample of known particle size. The determination of K was made at the point where half the total area under the spectrum resulted from the Zeeman pattern and the other half from the superparamagnetic fraction. Spectra used for such calculations are exemplified in Fig. 4. These spectra (28) were obtained from microcrystalline a-Fe203 produced by thermal decomposition of ferric nitrate on silica gel and subsequent... 

As will be seen below, the Neel temperature of these phases is very high (TN > 700 K). The Mossbauer spectra obtained at room temperature show two Zeeman patterns, once again corresponding to trivalent iron in octahedral and tetrahedral sites. Mossbauer data are reported in Table 2 and conclusions similar to those for the CaTi1 2yFe2y03 y can be drawn. For ordered structures (for instance y = 0.40 and y = 0.33, Fig. 14), the Fe(O)/ Fe(T) ratio is in perfect agreement with the ratio deduced from the predicted structures. 

Fig. 4.10. General appearance of MOV patterns for a Zeeman doublet. In the example shown here, the polarising optics were not perfect, which results in a Lorentz doublet superimposed on the centre of the rotation pattern (after J.-P.

Although all the examples chosen involve singlet states, for which the theory is especially simple, there is no problem in extending the method to more complex Zeeman patterns, or indeed in including the effect of Paschen-Back uncoupling on the MOV spectrum [166]. The influence of -mixing on MOV patterns has also been studied, and is in principle well understood [167], If the experiment is performed with lasers, the influence of laser power on Faraday rotation arises both by population transfer and by the Autler-Townes splitting (section 9.10) [173]. 

Zeeman splitting patterns for a number of elements together with their resonance lines are shown in Figure 13. 

The sensitivity obtained by transverse AC Zeeman AAS for the elements with the normal Zeeman pattern is good and often nearly the same as for the conventional AAS. In addition, for many elements with the anomalous Zeeman effect such as Ni, Mn, Sb, Tl, and Ag,... 

The three roots are Xi = 1, X2 = 0, and X3 = — 1 in units of g Hg. This situation corresponds to a conventional Zeeman pattern of the magnetic sublevels. If we call the diagonal eigenvalue matrix A then there is a matrix C for which... 

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