Optical dipole transition

The operator in the first temi goes as r, and is thus proportional to the optical dipole transition moment... 

Owing to the symmetry property of an optical dipole transition, the data analysis for a photodissociation study is greatly simplified. The center-of-mass differential cross-section for a single-photon, dissociative process can be expressed as38,39... 

In Section 15.3.3, we discussed the excitation of higher electronic states using laser light to drive optical dipole transitions. The interaction was strongly damped by spontaneous emission from the upper level indeed, the molecules were detected by means of the scattered photons. In this section, we consider some ways to manipulate the hyperfine sublevels within the ground state of the molecule. In contrast to optical transitions, the coherences between these ground-state levels are not radiatively damped. 

The selection rules applicable to optical dipole transitions also apply to X-ray transitions. The rules are AL = 1, Aj = 0, 1. Intensity rules are also the same as those applicable to optical transitions. The transitions obeying selection rules are called normal transitions. Not all transitions allowed by selection rules are observed. On the contrary, some transitions, which are not allowed by selection rules, are sometimes observed. These are called forbidden transitions. The observed lines were initially given names as per their observed line intensities. The Siegbahn notation used to name various observed lines is given in Table 1. As this nomenclature is intensity-based... 

Since the optical transitions near the HOMO-LUMO gap are symmetry-forbidden for electric dipole transitions, and their absorption strengths are consequently very low, study of the absorption edge in Ceo is difficult from both an experimental and theoretical standpoint. To add to this difficulty, Ceo is strongly photosensitive, so that unless measurements arc made under low light intensities, photo-induced chemical reactions take place, in some cases giving rise to irreversible structural changes and polymerization of the... 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

As shown in Fig. 7, a large increase in optical absorption occurs at higher photon energies above the HOMO-LUMO gap where electric dipole transitions become allowed. Transmission spectra taken in this range (see Fig. 7) confirm the similarity of the optical spectra for solid Ceo and Ceo in solution (decalin) [78], as well as a similarity to electron energy loss spectra shown as the inset to this figure. The optical properties of solid Ceo and C70 have been studied over a wide frequency range [78, 79, 80] and yield the complex refractive index n(cj) = n(cj) + and the optical dielectric function... 

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]. 

We see that the electric dipole allowed transitions are, in general, much more intense than the magnetic dipole allowed transitions. In fact, the magnetic dipole contribution to an optical transition of a center dominated by an electric dipole character is usually completely masked by the much more intense J 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). 

For the optical activity of achiral chromophores with a dissymmetric environment, two types of theoretical treatments have been proposed coupled oscillator treatment and one-electron treatment. The charge distribution of the magnetic dipole transition correlates Coulombically with an electric dipole induced in the substituents, and the colinear component of the induced dipole provides, with the zero-th order magnetic moment, a non-vanishing rotational strength. 

Electronic transitions are optically forbidden only for large intemuclear distances r. For finite r, dipole transitions to the X 2 ground state are possible. They give rise to the well-known Hopfield continuum and 600-A emission and absorption bands.86 Only those collision partners that surmount the barrier of the ungerade potential are likely to radiate. The cross section for light emission65 is typically 10-4 A2, which is much too... 

Dispersion interactions increase with the polarizability of the two molecules. The optical properties enter in the form of the excitation frequencies. Expression (6.9) only considers one term of a series over dipole transition moments. Usually, however, this term is by far the most dominant one. 

Fig. 3). Note that optical transitions between the two configurations are parity allowed as electric-dipole transitions. The spin-selection rule is relaxed by spin-orbit coupling, the more so the higher the principal quantum number is. Due to selection rules on AJ, the transitions 1S0-3F0 and 1S0-3P2 remain strongly forbidden. The emission is due to the 3P0,i >1 o transition. Whether 3P0 or 3Pj is the initial level depends on their energy difference and the temperature.

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