Perpendicular Zeeman effect

For the small magnetic field of 1 T the perpendicular Zeeman effect only slightly affects the energy, but does affect the wave functions largely. 

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). 

Transitions between the two spin states (+1/2 and -1/2) can be induced by oscillating electromagnetic radiation (v in the microwave region) applied perpendicularly to 77. The energy-level splitting is referred to as the Zeeman effect, illustrated in Figure 16.1. Normally in the EPR measurements, v is maintained at a fixed value and 77 is permitted to vary until the resonance is matched. 

We have calculated exactly the Zeeman effect for the levels IS, 3S and 3P. Indeed it is necessary to know the shift for all the hyperfine levels very well. These calculations are very classical and we just present the results in a Zeeman diagram (see Fig. 5). The most important part in the diagram is the crossing between the 38 2 (F=l, mp=-l) and 3P1/2(F=1, mj =0) levels, because the quadratic Stark effect is proportional to the square of the induced electric field and inversely proportional to the difference of energy between the two considered levels. Moreover the selection rules for the quadratic Stark effect in our case (E perpendicular to B) impose Am.F= l. So it is near this crossing that the motional Stark shift is large enough to be measured. In our calculations the Stark effect is introduced by the formalism of the density matrix [4] where the width of the levels are taken into account. The result of the calculation presented on... 

There are few published reports of experiments on the Zeeman effect in nitrogen quadrupole resonance. In her study of p-bromoaniline, Minematsu 41) showed that the Ox and Oy axes of the electric field gradient tensor lie in the molecule plane, with Oy being directed along the molecule axis of symmetry and Ox perpendicular to it. 

This would imply a very simple linear Zeeman effect but, as we show in chapter 8, additional terms describing the nuclear spin rotation interaction and the spin-spin interaction make the system much more interesting. The nuclear spin transitions are induced by an oscillating magnetic field applied perpendicular to the static magnetic field, the perturbation being represented, for example, by the term... 

Figure 11.24. Experimental arrangement used by Ernst and Kindt [44] in their pump/probe microwave/optical double resonance study of a rotational transition (18.2 GHz) in the ground state of CaCl. The photomultiplier tubes which monitor fluorescence are situated on the axis perpendicular to both the laser beam and the molecular beam. The C region, where the molecular beam is exposed to microwave radiation, is magnetically shielded to minimise stray Zeeman effects. The microwave power was amplitude modulated at 160 Hz and the modulated fluorescence detected by photomultiplier B. 

Pieter Zeeman was the first to study the effect of an applied magnetic field on atomic emission spectra. Since a perpendicular applied field was subsequently typically used within Zeeman (excited state emission) spectroscopy the normal Zeeman effect is usually described in terms of parallel (II) and perpendicular (J.) plane polarized bands (Figure 1). It should be noted, however, that Zeeman also studied the parallel magnet alignment used within MCD spectroscopy. In Zeeman s words during his Nobel prize lecture in 1902 describing results obtained for emission from the 5d orbital of Cd to the 5p orbital,. But let us first consider the rays... 

Figure 1 The normal Zeeman effect. The emission from an atomic lamp source placed within a magnet observed perpendicular (a) and parallel (b) to the lines of force. It should be noted that when 5 = 0 and the Russell-Saimders spin coupling mechanism is applicable, J = L, and Mj = Ml as shown here. (Reprinted from Mack, Stillman and Kobayashi, Elsevier 2007)...

Fig. III. 14. The effect of the translational Zeeman effect on the absorption spectra of symmetric top molecules moving at different velocities perpendicular to the exterior magnetic field is shown for the J = - J = 2, K =l rotational transition of methylacethylene (l Oj. = 0, 100, 200,. 800 m/sec). With increasing velocity the aligning force of the Lorentz cross field...

Fig. III. 16. In light symmetric top molecules with reasonably large electric dipole moments such as for instance methylfluoride the change of the absorption spectrum due to the translational Zeeman effect occurs at comparatively low perpendicular velocities. The spectrum shown here corresponds to the absorption of a group of molecules moving at 267 m/sec (maximum of the Maxwell-Boltzmann probability distribution) perpendicular to the magnetic field. The dotted line gives the spectrum calculated neglecting the translational Zeeman effect. The Lorentz cross field has caused considerable mixing of Mj substates resulting in considerable changes in the selection rules...

Other examples are provided by an orbit perpendicular to the direction of the field in the case of the Zeeman effect and, in the case of the problem of two centres ( 39), by one which is confined to the surface of an ellipsoid of rotation, etc. For the purpose of illustration we shall continue to speak of circular orbits, eccentricities,... 

On the other hand, a phase gap, 8, between the linear polarizations parallel (In) and perpendicular (I ) to the magnetic field may be induced when a transparent medium, placed in a magnetic field which can cause a Zeeman effect, is irradiated with light propagating perpendicularly to the lines of magnetic force. This phenomenon is known as the Cotton-Mouton effect (Voigt effect). The phase gap is given by Eq. (4.37),... 

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