Quadratic Stark effect

Applying McRae s equation, and neglecting the Stark-effect (quadratic) term the shift. A /, in the transition energy from the gas phase to that in a given solvent is expressed as ... 

Jones, 1 Roy. Soo. Proc., A, vol. 105, p. 650 (1924). The first attempt to calculate the mole refraction from the quadratic Stark effect formula was made by Lennard-Jones (Jones), with the old quantum theory, f Z. f. Physik, vol. 38, p. 518 (1926). 

Drobizhev M, Tillo S, Makarov NS, Hughes TE, Rebane A (2009) Color hues in red fluorescent proteins are due to internal quadratic stark effect. J Phys Chem B 113 12860-12864... 

Evaluation of second-order molecular hyperpolarizability using the quadratic Stark effect... 

Fig.7. Quadratic Stark effect spectrum of a poly(methylmetacrylate) film doped with an azobenzene-linked amphiphile C180AZ0C00H (solid line). Dotted line, broken line, and dash and dotted line show an absorption spectrum of the film, its first derivative, and second derivative, respectively.

The reason that I am elaborating in such detail on these c.t.s. s is that they are practically the only states in region 3, and also I believe that if we can only get a clear understanding of these states, the question of optical transition will sort itself out automatically. There are also many other effects in molecular complexesjyhere the c.t.s. s enter. I have already mentioned the cases of the quadratic Stark effect and of tfie asymmetric crystal field, where the c.t.s. s must be allowed to play an equally important and indeed analogous role. A further effect relates to the width of the charge transfer bands. The main cause of the breadth is essentially the same as that for the width of the crystal-field spectrum, except that it is much... 

Fig. 5.1. Hanle effect analogue in the case of the quadratic Stark effect.

As example of the employment of the density matrix method for calculation of observable signals, we propose to consider the quadratic Stark effect in the simplest case of the 1S states of molecules possessing a constant electric dipole moment dp. In an electric field the magnetic sublevel M of a rotational state J of such a molecule acquires additional energy [374] ... 

The prerequisite for the creation of orientation in the aligned state can also be formulated in terms of the time reversal properties of a Hamiltonian operator which represents the perturbation. As is shown in [276, 277] the alignment-orientation conversion may only take place if the time invariant Hamiltonian is involved. For instance, the Hamiltonian operator of the linear Zeeman effect is odd under time reversal and is thus not able to effect the conversion, whilst the operator of the quadratic Stark effect is even under time reversal and, as a consequence, the quadratic Stark effect can produce alignment-orientation conversion. 

Let us consider the situation [44] where an external stationary homogeneous electric field is applied along the 2-axis, Fig. 5.3. We will use the quadratic Stark effect energy expression in the form of (5.15), supposing 0q = 7t/4. The choice of azimuth angle (p value needs more discussion. First, one must remember that the Ir — Ii signal only appears if the orientation component along the direction of observation possesses non-zero... 

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... 

A Stark effect for adsorbed sulfate on Pt electrodes has been reported for the 1200 cm symmetric stretching mode of the adsorbed ion [165]. A quadratic dependence of the band center on the applied electric field is observed (Fig. 60). But this field dependence changes with the degree of coverage. The frequency values extrapolated to zero coverage (singleton frequency) present a linear dependence on the applied electric field (Fig. 61). So we conclude that the second-order Stark effect is induced when the ions are close together on the surface. 

Extensive theoretical studies of donor and acceptor spectra have shown that in semiconductors with a concentration of neutral impurities No and a concentration of ionized centres N, the increase of the line widths is proportional to (Ni/No)2 3 when linear Stark effect is present, to (Ni/No)4 3 when the quadratic Stark effect dominates, and to Nj/Nq when the quadrupole effect dominates [70,90]. 

Figure 8.38b gives an experimental display of the consequence of the quadratic Stark effect of the profile of the 3p i (P) line in a partially annealed NTD silicon sample. 

Fig. 8.38. Comparison of the profiles of the 3p i P line at LHeT in a NTD natSi sample with [P] —2 x 101Bcm-3 after (a) a post-irradiation 2-h annealing at 650° C and (b) a complementary annealing at 800° C, showing the effect of quadratic Stark effect in (a). The spectral range is 340.37-343.59 cm 1 and the resolution 0.06 cm-1 (7 ueV) (after [67]). Copyright 1981 by the American Physical Society...

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