Stark splitting

Measurements of Stark splittings in microwave and radiofrequency spectra allow tliese components to be detennined. The main contribution to tire dipole moment of tire complex arises from tire pennanent dipole moment vectors of tire monomers, which project along tire axes of tire complex according to simple trigonometry (cosines). Thus, measurements of tire dipole moment convey infonnation about tire orientation of tire monomers in tire complex. It is of course necessary to take account of effects due to induced dipole moments and to consider whetlier tire effects of vibrational averaging are important. 

With the aid of these above two equations, the linear Stark splitting can be evaluated as... 

By modulating the electric field and using phase-sensitive detection methods, Uehara et al. 8 ) were able to increase the sensitivity considerably and they could even detect Stark splittings of less than the doppler width of the components. Fig. 3 shows the Stark spectrum of HDCO for different electric field strengths. Because of the Stark modulation technique the absorption lines appear differentiated the zero points represent the center of each line. 

With this procedure, as with the double-resonance methods in atomic physics, Zeeman and Stark splittings, hyperfine structures and A doublings in molecules can be measured with high precision, even if the observed level splittings are far less than the optical dopp-ler width. From the width of the rf resonance and from the time response of the pumped systems, orientation relaxation rates can be evaluated for individual v J") levels. Other possible applications of this promising technique have been outlined by Zare 30) Experiments to test some of these proposals are currently under investigation and their results will be reported elsewhere. 

This method is specially suited for measurements of closely spaced Zeeman or Stark splitting and fine and hyperfine structures, which are separated only within their doppler linewidth 5 ). 

Detailed theoretical and experimental investigations 328-330) of such coupling effects show that they are not caused entirely by these hole-burning effects, but that double quantum Raman transitions occur and that the interaction between both light fields and the molecule via the common level leads to a dynamic Stark splitting of the probe line 33D. 

As a first example for the application of this technique, we mention the investigation of Stark splitting in molecules studied with a CO2 laser by Brewer etal. The authors shifted the vibration-rotation levels of by an external electric field. With increa-... 

Comparing two Stark compon ents with a common lower level and slightly different center frequencies (Au = 1.56 0.05 Mc/sec), it has been possible to measure the Stark splitting in the excited state and the ratio of the transition probabilities for both transitions. Since the isotopic abundance (and with it the density of Ni WjD molecules) is known, the absolute value of the transition moment can be estimated to 1X12 = 0.33 0.1 Debeye. 

Table 3. Stark splittings in pure quadrupole resonance (4)...

Table 3 shows measurements of this effect, taken from a paper by Dixon and Bloembergen (4). The experimental results are compared with calculated values of the effect of the electric field on the quadrupole resonance frequency in which it was assumed that no jr-bonding is present. These calculations are rather crude but predict the correct order of magnitude for the Carbon-Chlorine bond. For the SiCl bond, however, the experimental Stark splittings are both much less than those for the C—Cl bond and almost an order of magnitude less than the calculated value and once more a ready rationalisation of this phenomenon lies in An—pn bonding. 

The pre-pulse thus prepares the system in a state of maximum electronic coherence (see Figure 6.10b around t = -100 fs). Only 0.5% of the population escapes to the resonant target state 4). Transitions to the off-resonant target states 3) and 5) are completely suppressed since the dynamic Stark splitting of the... 

Nonradiative transitions can also occur between 4/ rare-earth levels. Orbit-lattice interaction may induce these between two stark-split components of the same 4fN term or between stark-split components of different 4fN terms. One assumes that the crystal field the ion sees is modulated by the vibrations of the surrounding ions. If the spacing between the two 4fN levels is less than the Debye cut-off frequency, there will be acoustical phonons capable of inducing direct transitions between the levels. The theoretical treatment of this problem is quite complex (36). 

The theoretical energy values for 3H4, JG4, JD2 are shown in tables 10-12 together with the observed values and the values obtained by semiempirical calculations based on crystal field theory (Faucher and Moune, 1997). T s are the irreducible representations in S4 symmetry. The possible irreducible representations are l i. r2, r3, r4 for a two-electron system where r3 and F4 are degenerate. The theory overestimates Stark splittings of the 3H4 level, compared to the experimental values. One reason for this is the neglect of lattice relaxation... 

The theoretical energy levels of the ground state 4Ig/2 are shown in table 13 together with the results of CF calculations and the experimental values. Among the irreducible representations of S4 symmetry, only I 5. Te, T7, Fg are possible for a three-electron system, where I 5 and 17, or F7 and Tg are degenerate. Comparing with the experimental values, the Stark splittings are somewhat overestimated. However, the order of irreducible representations of these five levels is consistent with both the experimental values and those obtained by CFT. 

Photoluminescence excitation spectroscopy (PLE) was performed on GaN Er by several groups [15-17], FIGURE 2 shows typical PLE spectra probing the second and third excited Er states while monitoring the 1.539 pm PL line. The Stark splitting caused by the crystal field is clearly shown. The excitation source was 250 mW from a tunable Ti sapphire laser. 

Figure 8.32. Strong field levels for the J = 1 level in CsF. An electric field produces the Stark splitting between the Mj = 0 and 1 components, and 133Cs quadrupole interaction sphts each Stark component into four levels. Each level is two-fold degenerate the two components are labelled by their values of Mj and Mjx. The eight electric dipole transitions which become allowed in the electrostatic C field are shown.

In subsequent work the corresponding spectrum of IO was observed and analysed [21] the dipole moments of BrO and IO [29] were also determined from Stark splittings... 

Whichever method is used for modulation, it also possible to measure the electric dipole moment of the molecule under investigation. This can be achieved either by measuring the separation between the unshifted and Stark-shifted lines as a function of the modulation amplitude, or by direct measurement of the Stark splitting produced by a static electric field. 

Figure 10.20. Field strength distribution in the cathode plasma sheath above a bare and a diamond-coated Si substrates for Kh = —200 V. The field strength was evaluated from the Stark splitting (broadening) of the Hoi and Hp lines [234].

An array of charges in a crystal produces an electric field at any one ion, the so-called crystalline electric field. The presence of this field causes a Stark splitting of the free ion energy levels which results in a substantial modification of magnetic, electrical and thermal properties of the material. The theory of the crystal field and its interpretation in terms of group theory are originally due to Bethe (16). 

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