Zeeman Broadening

A final way of measuring stellar fields is by looking at the overall broadening of spectral lines of different Lande factor and Zeeman structure to discover broadening in excess 

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Stark and Zeeman broadening caused by electric and magnetic fields respectively set up within the sample vapour and which perturb atomic energy levels. 

The characteristic spread in magnetic field is given by AB = kBT/jv For a temperature of 1 mK, AB = 1.6xlO 3T, and the spread in vz is Avz = 300 Hz. For a temperature of 30 pK the linewidth is 10 Hz. Thus, Zeeman-broadening in the trap is potentially significant However, as described below, it is reduced by motional averaging effects. 

Zeeman broadening can be reduced by motional averaging providing that the rate at which the atom transverse the trap is large compared to the Zeeman frequency spread. The average linewidth is given by... 

Figure Bl.12.1. (a) Energy level diagram for an/= nueleus showing the effeets of the Zeeman interaetion and first- and seeond-order quadnipolar effeet. The resulting speetra show statie powder speetra for (b) first-order perturbation for all transitions and (e) seeond-order broadening of the eentral transition, (d) The MAS speetnim for the eentral transition. ...

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). 

We have seen in Chapter 2 that the electronic Zeeman term, the interaction between unpaired electrons in molecules and an external magnetic field, is the basis of EPR, but we have also discussed in Chapter 4 the fact that if a system has more than one unpaired electron, their spins can mutually interact even in the absence of an external field, and we have alluded to the fact that this zero-field interaction affords EPR spectra that are quite different from those caused by the Zeeman term alone. Let us now broaden our view to include many more possible interactions, but at the same time let us be systematic and realize that this plethora of possibilities is eventually reducible to five basic types only, two of which are usually so weak that they can be ignored. 

Fig. 2. Absorption spectrum of CjHs obtained with the Zeeman-tuned He-Ne laser line at X = 3.39 fim. The dips in the transmission of magnetic field dependent laser intensity are due to different rotational transitions in CjHj, their width is determined by doppler broadening. (From Gerritsen, H.J., ref.

A high-resolution spectrum of the clock transition is shown in Fig. 2. The clock-laser power was reduced to 30 nW to avoid saturation broadening. The fit with a lorentzian curve results in a linewidth of 170 Hz (FWHM), corresponding to a fractional resolution bv/v of 1.3 10-13. A spectral window of 200 Hz width contains 50% of all excitations. According to our present experimental control of the ion temperature, electromagnetic fields and vacuum conditions, no significant Doppler, Zeeman, Stark or collisional broadening of the absorption spectrum of the ion is expected beyond the level of 1 Hz. The linewidth is determined by the frequency instability of the laser and the lineshape is not exactly lorentzian... 

In order to identify the location of the carbon sources, Zeeman spectroscopy has turned out to be a valuable tool. The principles of the influence of the magnetic field on carbon and oxygen ions in the fusion edge plasma (B = 1 to 10 T) have been outlined in [19,20]. The method works well when the Zee-man (Paschen-Back) effect plays an important, or dominant, role in relation to other broadening mechanisms. In general the line splitting is given by ... 

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