Zeeman parallel

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 influence of a magnetic field on gaseous atoms induces a splitting of each line into several polarised components. This phenomenon, which can be seen in the emission or absorption spectra of these atoms and is called the Zeeman effect, arises from perturbations in the energy states of electrons in the atom (Fig. 14.13). For example, the absorption wavelength of cadmium, situated at 228.8 nm, leads to three polarised absorption bands due to the Zeeman effect. One of these bands, the it component, retains the initial value of the wavelength whereas the other two, the a components, are symmetrically shifted by a few picometres relative to the 7r component in a 1-tesla field. The direction of polarisation of the 7r and a lines are perpendicular and the polarisation plane of the 7r component is parallel to the magnetic field (Fig. 14.14). 

The programming of the formulae needs a COMPLEX 16 arithmetic since the CF potential itself could be complex. Therefore, it is easy to implement the complex spherical transforms of the magnetic field, x and B, into the (complex) Zeeman matrix elements. With the magnetic field Eref aligned parallel to the principal rotational axis of an axial system, the Zeeman matrix stays real since then B](] = Bxef. Its counterpart for the perpendicular direction is also real, and this involves the following transforms x = - (l/V2)Bref and... 

The calculations in the complete d2 space spanned by 45 functions show (Fig. 121) that the lowest multiplet is a nonmagnetic singlet A separated from another nonmagnetic singlet A by an energy gap 834/hc = 13 cm 1 (Fig. 27). This has no parallel to the traditional SH ZFS. Both these singlets, however, possess some quadratic Zeeman coefficients, and the susceptibility components show a complex temperature dependence (Fig. 29). 

There are several other important aspects of the experiment which should be mentioned. The waveguide cell is surrounded by a solenoid coil which can produce a magnetic field parallel to the ion beam direction the magnitude of this field (up to 50 G) is often sufficient to produce observable Zeeman splittings which greatly assist spectroscopic assignment, as we will see. ft is also possible to expose the molecular ion beam to two different microwave frequencies this so-called double resonance technique enables two different microwave transitions to be connected, if they share a... 

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,... 

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