Hanle signal

The determination of the concentration dependence of the width of the Hanle signal is widely used for measuring the relaxation cross-section of alignment <72, applying (2.42), where K = 2. As an example we may quote data from [312] given in Fig. 4.8, where a very large value of 02 = 1000 A2 was obtained for collisions K2(B1IIU) + K. 

Fig. 4.7. Calculated Hanle signal curves for P, R transitions (a) linear polarized excitation (Fig. 4.2,

Fig. 4.8. Hanle signal from a K2(l 1nu) molecule (weak excitation) (a) and dependence of relaxation rate r2 on potassium atom concentration (b).

Note that the superpositional Hanle signal, reflecting overlapping of effects from both levels, coupled with optical excitation, is sensitive to the signs of the Lande factors gj> and gj even with Lorentzian geometry, where

linear Hanle effect. This is easily understood, since there is a large difference between the cases... 

Let us turn to experimental investigations. The ground state Hanle signal was registered on Na2(.X 1 +), K2pT1E J ) [149, 152] for linearly polarized Q-excitation under conditions close to those given in Fig. 4.9. In particular, the detailed studies [12, 18] clearly demonstrated a narrow... 

If we assume the lower level Lande factor as known, then the fit of non-linear Hanle signals permits us to determine the relaxation constants 7K = 7, as well as the effective cross-sections light field, which mixes the multipole moments aPq with different k, does not permit us to determine the values for definite k separately. Nevertheless (Section 3.3), the discrepancies between the 7K values are negligible in many cases, and the information obtained is sufficiently reliable. 

What kind of information do these Hanle signals contain Fig. 4.15 might help to make this clear. There we see the expected shape of the Hanle signals at toj< = u>j and at j>F = j/T. The curves 1 (Ei E) and... 

Fig. 4.15. Hanle signals produced by the probe beam at fluorescence pumping.

This leads to the manifestation of the non-linear Hanle effect in the ground state (the observed signal is proportional to T2). The non-linearity of the effect is not obvious in this case and consists of the following fact. Despite the fact that the approximation (5.63), (5.64), (5.65) and (5.66) is linear with respect to the light field (proportional to Tp), it is necessary for observation of the Hanle signal (5.61) to calculate the second (2) (i)... 

Fig. 7.2 Level-crossing spectroscopy (a) experimental arrangement (b) level scheme and (c) Hanle signal...

Fig. 7.4 Hanle signal of the fluorescence from laser-excited Na (B 77 , v = 10, J = 12) molecules (a) schematic experimental setup for difference and ratio recording and (b) measured...

The transformation (t — to) f of the variable to shifts the integration limits to the interval from f = oo to t = 0, which shows that the integral is independent of t. It can be solved with the substitution 2 sin x = 1 - cos2x, which yields the Hanle signal, observed by the detector Di in Fig. 7.4a ... 

For illustration, a molecular Hanle signal is depicted in Fig. 7.4 that was obtained when Na2 molecules were excited in a magnetic field B into the upper level 2) = B IJj (v = 10, J = 12) by an argon laser at A. = 475 nm [835]. For this Na2 level with S = 0 Hund s coupling case applies, and the Land6 factor... 

In larger molecules the phase-coherence time of excited levels may be shorter than the population lifetime because of perturbations between closely spaced levels of different electronic states, which cause a dephasing of the excited-level wave functions. One example is the NO2 molecule, where the width of the Hanle signal turns out to be more than one order of magnitude larger than expected from independent measurements of population lifetime and Landd factors [851, 852]. This discrepancy is explained by a short intramolecular decay time (dephasing time), but a much larger radiative lifetime [853]. 

What is the width AB1/2 of the Hanle signal from the crossing of the two Zee-man components of one of the hyperfine levels F = 3 or F = 2 in the ground state 5 5 i/2 of the rubidium atom I Rb with a nuclear spin I = 5/2, if the mean transit time of the atoms in a buffer gas through the excitation region is F = 0.1 s Explain why this method allows the realization of a sensitive magnetometer (see also [867]). 

If a second detector is placed in the x-direction with a polarizer having the angle against the y-axis, the measured Hanle signal is ... 

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