Forced-electric dipole

Finally, we should remember that f f transitions are parity-forbidden. However, most of them become partially allowed at the electric dipole order as a result of mixing with other orbitals that have different parity because of a noninversion symmetry crystal field (see Section 5.3). Thus, a proper choice of the crystal host (or the site symmetry) can cause a variety of (RE) + transitions to become forced electric dipole transitions. 

After X-ray irradiation of thermally annealed NaCl crystals, a small percentage of divalent europium ions are converted into trivalent europium ions (Aguilar et al, 1982). This is shown by the appearance of weak and narrow absorption lines at around 460 nm and 520 nm, related to the Fq D2 and Fq Di transitions of Eu + ions, respectively. For our purposes, this example allows us to compare the different band features between (RE) + and (RE) + ions Eu + ions show broad and intense optical bands (electric dipole allowed transitions), while Eu + ions present narrow and weak optical lines (forced electric dipole transitions). 

Forced electric dipole emission occurs if it is possible to mix even functions into the uneven 4/ functions, so that the parity selection rule is relaxed. It is usually assumed that this occurs by 4f—5d mixing. For Eu +, however, the 4/ 5high energy (see Table 3). Since the electric-dipole emission dominates for Eu3+ on sites without inversion S5unmetry, it seems obvious to assume that another state is used to relax the parity selection rule. This must occur by mixing the 4/ configuration with the levels of opposite parity of the c.t. state. 

Similar results have been reported for Eu3+ in glasses (J4) germanate glasses where the Eu3+ c.t. band is situated at 38462 cm i show a more intense forced-electric-dipole emission than phosphate glasses, where the c.t. band lies at 49020 cm i. These excimples illustrate the influence of the c.t. state upon the Eu3+ 4/- 4/ emission. 

The crystal field model may also provide a calciflation scheme for the transition probabilities between levels perturbed by the crystal field. It is so called weak crystal field approximation. In this case the crystal field has little effect on the total Hamiltonian and it is regarded as a perturbation of the energy levels of the free ion. Judd and Ofelt, who showed that the odd terms in the crystal field expansion might connect the 4/ configuration with the 5d and 5g configurations, made such calculations. The result of the calculation for the oscillator strength, due to a forced electric dipole transition between the two states makes it possible to calculate the intensities of the lines due to forced electric dipole transitions. 

The characteristic absorption and emission spectra of lanthanide compounds in the visible, near ultra-violet and infra-red is attributed to transitions between 4/ levels due to the fact that they present a sharp line with oscillators strengths typically of the order of 10 . These transitions are electric dipole forbidden but became allowed as forced electric dipole transitions. 

The forced electric dipole mechanism was treated in detail for the first time by Judd (1962) through the powerful technique of irreducible tensor operators. Two years later it was proposed by Jorgensen and Judd (1964) that an additional mechanism of 4/-4/ transitions, originally referred to as the pseudo-quadrupolar mechanism due to inhomogeneities of the dielectric constant, could be as operative as, or, for some transitions, even more relevant than, the forced electric dipole one. 

The first known work on the intensities of the intra 4f—4f transitions is that of Van Vleck [53]. This was followed by the work of Jurbner and coworkers [54,55]. In 1962 Judd [56] and Ofelt [57] independently proposed the theory of forced electric-dipole transition which enabled the compilation of oscillator strengths for lanthanide aquo ions. 

Empirical correlation of intensities of absorption bands with the structure of complexes in solutions have been made for lanthanide complexes. It has been recognized that forced electric-dipole transitions of low intensities, in some cases lower in intensity than those of magnetic-dipole transitions, may indicate that the ligand field has point group symmetry with a center of inversion. This criterion has been used in the determination of the ligand field by symmetry of Eu3+ aquo ion [202], The absorption band intensity ratios have been used to show the octahedral structure [49] of lanthanide hexahalide complexes, LnXg. ... 

The narrow absorption and emission bands of rare-earth 0-diketonates in the visible, near ultra-violet and near infra-red is attributed to 4f-4f transitions. These transitions are electric dipole forbidden to first order, but are allowed by the electric quadrupole, vibronic, magnetic dipole and forced electric dipole mechanisms. The magnetic dipole character of the Dq F transition of the Eu + ion was demonstrated in 1939 by... 

Table 5 also gives the contributions from the forced electric dipole mechanism... 

Judd 14) has applied the forced electric dipole mechanism to transitions within the / -electron configuration and was able to develop an expression for the oscillator strength of a given transition. (For purposes of comparing results we have defined = (2/ - - 1) where is the term used in Judd s paper 2,14).)... 

Forced Electric Dipole Transitions. In more recent work, Judd (15) has given further attention to the problem of intensities. According to this work, under certain symmetry restricted circumstances, the Hamiltonian for the interaction of a lanthanide ion with its neighbors can contain spherical harmonics with fc = 1 if the electrons of the rare-earth ion produce an electric field at the nucleus that exactly cancels that... 

The model which has been most widely applied to the calculation of vibronic intensities of the Cs2NaLnCl6 systems is the vibronic coupling model of Faulkner and Richardson [67]. Prior to the introduction of this model, it was customary to analyse one-phonon vibronic transitions using Judd closure theory, Fig. 7d, [117] (see, for example, [156]) with the replacement of the Tfectromc (which is proportional to the above Q2) parameters by T bromc, which include the vibrational integral and the derivative of the CF with respect to the relevant normal coordinate. The selection rules for vibronic transitions under this scheme therefore parallel those for forced electric dipole transitions (e.g. A/ <6 and in particular when the initial or final state is /=0, then A/ =2, 4, 6). 

In his calculation of the induced dipole-dipole and dipole-quadrupole processes of energy transfer Kushida (17) made use of the Judd-Ofelt1) expression for the forced electric dipole transition probability in the rare earths incorporated in solids. 

Note that the excited state has a component. It turns out that strong transition intensities in the lanthanides occur due to a transition termed "forced-electric-dipole" transitions, where AJ s 2. This rule holds in all cases where strong intensities have been observed. Thus, for our case, the transition involves the 6H13/2 state, because of the AJ = 2 restriction. 

If there is no inversion symmetry at the site of the rare-earth ion, the uneven cry.stal field components can mix opposite-parity states into the 4/"-configurational levels (Sect. 2.3.3). The electric-dipole transitions are now no longer strictly forbidden and appear as (weak) lines in the spectra, the so-called forced electric-dipole transitions. Some transitions, viz. those with AJ = 0, 2, are hypersensitive to this effect. Even for small deviations from inversion symmetry, they appear dominantly in the spectrum. 

In NaGd02 Eu " the Dd- I 2 emission transition dominates, but other lines are also present. The Eu case is so illustrative, because the theory of forced electric-dipole transitions [8] yields a selection rule in case the initial level has J - 0. Transitions to levels with uneven J are forbidden. Further J = O->J = 0is forbidden, because the total orbital momentum does not change. This restricts the spectrum to D()- Fi, present as magnetic-dipolc emission, but overruled by the forced electric-dipole emission,... 

Do— F2, a hypersensitive forced electric-dipole emission, which indeed is dominating,... 

This is due to the calcite structure of InBQs which places Tb on a site with inversion symmetry which forbids the forced electric-dipole transitions (Sect. 2.3.3). An important criterion in the final phosphor selection is their degradation behavior in the tubes under high-density excitation [11]. 

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