Stark levels splitting

Thus, the excited state " Gs/2 (or splits into three Stark levels in Dj symmetry, labeled by 1/2, 1/2. and 3/2. while the terminal state //9/2 (or splits into live Stark levels, 1/2, 1/2, 1/2, 3/2, and E-ij2. In fact, the five peaks observed in the emission spectrum of Figure 7.9 are related to these five terminal levels. This is because, at the low temperature (10 K) of the spectrum, radiative transitions only depart from the lowest level of the excited state. 

Fig. 3. Stark modulation spectrum of HDCO around 2850.62 cm", obtained with a Zeeman-tuned Xe laser line at 3.50 fim. The Stark field is perpendicular to the optical field and increases from the bottom towards the top of the figure resulting in an increasing splitting of the Stark levels therefore more and more components are separated. (From Uehara, K.T., Shimizu, T., Shimoda, K., ref. 85))...

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. 

Fig. 6.13 Part of the excitation spectrum oftheNaw = 29 Stark levels from the 3d state in an electrostatic field of 20.5 V/cm corresponding to nj values of n — 3, n — 4, and n — 5. The energy splitting between m = 0 (highest energy fine in the doublets) and m = 1 states is of the order of 180 MHz. The arrows indicate theoretical positions of energy levels obtained by a numerical diagonalization of the Stark Hamiltonian (from ref. 28).

In order to determine into how many Stark terms a given energy level splits when put into a ligand field without making a detailed calculation of the values, the group-theoretical methods of Bethe (66) are convenient. In this method it is noted that the spherical harmonics transform according to the Ith irreducible repre-... 

It is well-known that the electron repulsion perturbation gives rise to LS terms or multiplets (also known as Russell-Saunders terms) which in turn are split into LSJ spin-orbital levels by spin-orbit interaction. These spin-orbital levels are further split into what are known as Stark levels by the crystalline field. The energies of the terms, the spin-orbital levels and the crystalline field levels can be calculated by one of two methods, (1) the Slater determinantal method [310-313], (2) the Racah tensor operator method [314-316]. 

The free-ion levels of an odd fN configuration (which are half-integral 7 s) in any noncubic symmetry are split by crystal field into levels that are doubly degenerate, the so-called Kramer s doublets. Thus each J level (j for one-electron) splits into (J + 1/2) Stark levels in D3h symmetry. 

The earliest pulsed laser quantum beat experiments were performed with nanosecond pulses (Haroche, et al., 1973 Wallenstein, et al., 1974 see review by Hack and Huber, 1991). Since the coherence width of a temporally smooth Gaussian 5 ns pulse is only 0.003 cm-1, (121/s <-> 121 cm"1 for a Gaussian pulse) nanosecond quantum beat experiments could only be used to measure very small level splittings [e.g. Stark (Vaccaro, et al., 1989) and Zeeman effects (Dupre, et al., 1991), hyperfine, and extremely weak perturbations between accidentally near degenerate levels (Abramson, et al., 1982 Wallenstein, et al., 1974)]. The advent of sub-picosecond lasers has expanded profoundly the scope of quantum beat spectroscopy. In fact, most pump/probe wavepacket dynamics experiments are actually quantum beat experiments cloaked in a different, more pictorial, interpretive framework,... 

It turns out that the spin and orbit numbers are actually the degeneracy of the energy levels in question and that they represent the possible Stark State splitting pointed out in a previous chapter. The fuU set of mlues are shown in the following Table, namely-... 

Lanthanide impurity-ion spectra consist of a series of sharp lines that appear in groups of closely spaced sublevels that correspond to transitions between crystal-field split free-ion levels. The simplest absorption spectra occur at very low temperatures ( 4K), at which only the lowest Stark level is populated, in general. As the temperature is raised, transitions originating from thermally accessible excited levels are possible, thus complicating the spectrum. In fluorescence spectra, transitions arise at low temperature only from the lowest lying sublevel of the excited free-ion level. At higher temperatures, other transitions become possible. 

An analysis of radio frequency transitions, occurring within individual rotational levels split by the Stark effect in external electric fields, yields fi = ( )0.30818 with an uncertainty of 0.01% [45]. 

Our perturbation calculation indicates that the w = 2 level splits into three levels under the influence of an electric field. Since this splitting occurs to first order, it is sometimes called a first-order Stark ejfect. Since x is proportional to F, the splitting is linear in F, as indicated in Fig. 12-6. 

Up to this point, we have not talked about the physical origin of the crystal-field effects. All we can say is that they look like Stark effects splitting of the (2J + 1) degenerated levels of the trivalent rare-earth ions. 

Figure 9.24 shows part of the laser Stark spectrum of the bent triatomic molecule FNO obtained with a CO infrared laser operating at 1837.430 cm All the transitions shown are Stark components of the rotational line of the Ig vibrational transition, where Vj is the N-F stretching vibration. The rotational symbolism is that for a symmetric rotor (to which FNO approximates) for which q implies that AA = 0, P implies that A/ = — 1 and the numbers indicate that K" = 7 and J" = 8 (see Section 6.2.4.2). In an electric field each J level is split into (J + 1) components (see Section 5.2.3), each specified by its value of Mj. The selection mle when the radiation is polarized perpendicular to the field (as here) is AMj = 1. Eight of the resulting Stark components are shown. 

In contrast to channel I, which remains non-degenerate in the field, channel II splits into three dissociation branches due to the Stark effect. Atomic calculations of the H atom in a cylindrical potential oriented along the z-axis show that the energy levels of 2p-orbitals split and H(2pj.) becomes more stable relative to H(2p c) and H(2py). Because of the lateral symmetry of the potential, the degeneracy of H(2pJ and H(2py) persists. For small values of w, H(2s) is slightly less stable than H(2p ) and H(2py) while the ordering reverses when w exceeds 0.15 a.u. As a result, there exist three dissociation limits for channel II, with a nonzero cylindrical potential, which correspond to H(2s), H(2pj,), and H(2p )/H(2py). 

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. 

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). 

An external electric field leads to three alterations in the electron structure of an atom. Firstly, the energy levels of the atom are shifted and split (the Stark effect). The theory of this effect is well-known [8], Secondly, the highly excited states of the atom disappear. The potential for the outer electron of the highly excited atom, is equal to... 

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