Level crossing Stark-Zeeman

We will conclude this section by illustrating how the tensor Stark polarizability constant can be measured using level-crossing spectroscopy. As illustrated in Fig.9,18, for the case of the potassium 5d 03/2 state the unknown Stark effect is measured in terms of the well-known Zeeman effect... 

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... 

In order to show that the translational Zeeman effect is negligible, we take an average translational velocity, Fq =yA TjM, which at T = — 60 °C leads to Fo=201 m/sec for ethylene oxide. At 25 kGauss this corresponds to a cross field Fts of 5 V/cm. With b = l-88 Debye for ethylene oxide, tlus leads to an estimate of the Stark effect energy, < ts > = lyMb TsI =4.7 MHz. We now take the most critical case, the Stark effect perturbation of the loi and lio rotational levels respectively, where the rotational energy difference in the denominator is smallest (11.4 GHz), and we get a second order perturbation in the order of 2 kHz which may come into the range of the experimental accuracy of... 

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