Induced electric dipole transitions

In much the same way as Stevens operators, the summation in Equation 1.15 is limited to well-defined values for f-electrons, the restriction k <7 holds, while q is limited to those values consistent with the point symmetry of the site. Finally, the even part k = 0, 2,4,6) is responsible for the CF splitting, while the odd part k = 1,3, 5,7) is responsible for the intensity of induced electric dipole transitions in optical spectroscopy [5b, 26]. 

X being a 4/ wave function. From this expression, one estimates that the oscillator strengths should be about the same as for an ion situated in a noncentrosymmetric field (P 10 6). A rigorous formal treatment for the vibronically induced electric-dipole transitions has been developed by Satten (32-34),... 

Judd (13) has shown that the oscillator strength of an induced electric dipole transition may be related to the energy of the transition (v, in cm. ") and the square of the matrix elements of the unit tensor operators connecting the initial and final states via three phenomenological parameters T (A = 2, 4, and 6) according to Equation 2. 

A. Electron-Phonon Interaction Parameterization Scheme. In observing the fluorescence decay rate from a given J-manifold, it is generally found that the decay rate is independent of both the crystal-field level used to excite the system and the level used to monitor the fluorescence decay. This observation indicates that the crystal-field levels within a manifold attain thermal equilibrium within a time short compared to the fluorescence decay time. To obtain this equilibrium, the electronic states must interact with the host lattice which induces transitions between the various crystal-field levels. The interaction responsible for such transitions is the electron-phonon interaction. This interaction produces phonon-induced electric-dipole transitions, phonon side-band structure, and temperature-dependent line widths and fluorescence decay rates. It is also responsible for non-resonant, or more specifically, phonon-assisted energy transfer between both similar and different ions. Studies of these and other dynamic processes have been the focus of most of the spectroscopic studies of the transition metal and lanthanide ions over the past decade. An introduction to the lanthanide work is given by Hiifner (39). 

It is important to realize that the dipole strength for MD fransifions are five orders of magnifude smaller than for fhe allowed ED fransifions. However, fhe induced electric dipole transitions in lanthanides are of fhe same magnifude as fhe magnetic dipole transitions. 

Within the frame of Judd-Ofelt theory, the intensity matrix element of an induced electric dipole transition is given by Gorller-Walrand and Binnemans (1998) and Judd (1962) ... 

Induced electric dipole transitions occur much more frequently than magnetic dipole transitions and therefore the largest part of this review is devoted to the former. However, induced electric dipole transitions have the disadvantage that the knowledge of wavefunctions is not sufficient for the calculation of electric dipole intensities and a parametrization is necessary. Judd and Ofelt developed independently the theoretical background for the calculation of the induced electric dipole matrix element. Their work is known under the common name Judd-Ofelt theory (sections 5 and 7). The papers of Judd... 

The intensities of the majority of the f-f transitions vary only within a factor of 2-3 from host matrix to host matrix, but some transitions are much more host dependent. These transitions are called hypersensitive transitions. These induced electric dipole transitions obey the selection rules for electric quadrupole transitions and are therefore sometimes called pseudo-quadrupole transitions. In sect. 8, we will discuss hypersensitivity in detail. The dependence of the Qx intensity parameters on the host matrix is the subject of sect. 9. Two-photon spectra (sect. 10) and vibronic transitions (sect. 11) are discussed briefly. On the other hand, chiroptical methods will not be considered. Since the color of the lanthanide ions is related to the spectral intensities of f-f transitions, we want to give attention to the phenomenon of color (sect. 12). Finally, the intensities of actinide ions are reviewed (sect. 13). 

The majority of the observed optical transitions in lanthanide ions are induced electric dipole transitions. An electric dipole transition is the consequence of the interaction of... 

The electric quadrupole transition arises from a displacement of charge that has a quadrupolar nature. An electric quadrupole consists of four point charges with overall zero charge and zero dipole moment. It may be pictured as two dipoles arranged so that their dipole moments cancel. An electric quadrupole has even parity. Electric quadrupole transitions are much weaker than magnetic dipole and induced electric dipole transitions. At this moment no experimental evidence exists for the occurrence of quadrupole transitions in lanthanide spectra, although some authors have claimed the existence of such transitions (e.g. Chrysochoos and Evers 1973). However, the so-called hypersensitive transitions (see sect. 8) are eonsidered as pseudo-quadrupole transitions, because these transitions obey the selection rules of quadrupole transitions. 

For instance, the dipole strength of an induced electric dipole transition of an oriented molecule with its x-axis parallel to the electric field vector is given by ... 

The dipole strength of an induced electric dipole transition is proportional to the square of the matrix element in the dipole operator and therefore also to the square of the electric field at the lanthanide site. However, in intensity studies, the lanthanide ions are not in a vacuum, but embedded in a dielectric medium. The lanthanide ion in a dielectric medium not only feels the radiation field of the incident light, but also the field from the dipoles in the medium outside a spherical surface. The total field consisting of the electric field E of the incident light (electric field in the vacuum), plus the electric field of the dipoles is called the effective field eff> i e. the field effective in inducing the electric dipole transition. The square of the matrix element in the electric dipole operator has to be multiplied by a factor E fflEf. In a first approximation, ( efr/ = ( + 2) /9. The factor (n + 2fl9 is the Lorentz local field correction and accounts for dipole-dipole corrections. 

Dipole strength of an induced electric dipole transition (single line and oriented system)... 

Selection rules for induced electric dipole transitions... 

From eq. (143) selection rules for induced electric dipole transitions can be derived ... 

The intensity parameters are now 2x (A=2,4,6) and they represent the square of the charge displacement due to the induced electric dipole transition. However, when transforming other parameters into the 2x parameters one has to be very careful. One must check the expression for the oscillator or dipole strength to see which factors are included into the parameter and which not. In particular, see whether the factor (2J +1) is included or not. Some authors write Tx when they mean 3x- The conversion between the Qx and 3x parameters is... 

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