Forbidden optical transition

However, the frequency area involved in the design of an atomic clock was changed recently in a radical way. Equation 11.1 shows that the performances of atomic clocks can be improved when the nominal frequency is increased toward the optical domain. Forbidden optical transitions (with a very weak excitation probability) have narrow natural line widths (ca 1 Hz), resulting in a high Q-factor (cfl 10, at frequencies of several hundreds of terahertz). During the past ten or so years, many projects for optical atomic clocks have been initiated. Laser cooling... 

R.G. Bray, W. Henke, S.K. Liu, R.V. Reddy, M.J. Berry, Measurement of highly forbidden optical transitions by intracavity dye laser spectroscopy. Chem. Phys. l tt. 47,213 (1977)... 

FIGURE 22.3 Energy levels and associated optical transitions of positive polaron and bipolaron excitations. The full and dashed arrows represent allowed and forbidden optical transitions, respectively. H, S, and L are HOMO, SUMO, and LUMO levels, respectively, and u and g are odd and even parity representations, respectively. 2too(P) and 2o)o(BP) are assigned. (From Vardeny, Z.V. and Wei, X., Handbook of conducting polymers, 2nd ed., eds. T.A. Skotheim, R.L. Elsenbaumer, and ]. Reynolds, Marcel Dekker, New York, 1998. With permission.)... 

Fig. 18. Schematic electronic structures (a) neutral polymer (b) positive polaron (c) negative polaron (d) positive bipolaron (e) negative bipo-laron (f) neutral soliton (g) positive soliton (h) negative soliton. CB, conduction band VB, valence band. The full and dashed arrows represent allowed and forbidden optical transitions, respectively.

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

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... 

The induced absorption band at 3 eV does not have any corresponding spectral feature in a(co), indicating that it is most probably due to an even parity state. Such a state would not show up in a(co) since the optical transition IAK - mAg is dipole forbidden. We relate the induced absorption bands to transfer of oscillator strength from the allowed 1AS-+1 (absorption band 1) to the forbidden 1 Ak - mAg transition, caused by the symmetry-breaking external electric field. A similar, smaller band is seen in EA at 3.5 eV, which is attributed to the kAg state. The kAg state has a weaker polarizability than the mAg, related to a weaker coupling to the lower 1 Bu state. 

In addition to the block, which consists of four vertical transitions, corresponding to the four-level model (j, l < 1 m = n = 0), there are also four pairs of transitions, which correspond to the two spectral doublets P-Q (j = 0,1 m = 0 / = 1 n = 1) and Q-R (j = 1, m = 1 l = 0,1 n = 0). So, each of these doublets is doubly degenerate and transforms with increase of x 1 independently of the other and of the spectral triplet of the four-level problem. Transitions between levels j = l = 1, m = n = 1 are forbidden optically and they are not connected by relaxation with the other ones. Therefore they do not appear in the spectrum even if interaction of the rotator with the orienting field is taken into account thus they may be excluded from further consideration. 

An additional advantage of ESA and ESE is the possibility of localizing high energy levels, which could not be accessed using conventional spectrophotometers. This is the case for some bands in the ultraviolet spectral region. Moreover, ESA could allow the observation of optical transitions, which are forbidden by one-photon spectroscopy (Malinowski et al, 1994)... 

Ti + belongs to the d configuration, which is the simplest one. The free ion has fivefold orbital degeneracy ( D), which is spht into two levels E and T2) in octahedral symmetry, which is quite common for transition metal ions. The only possible optical transition with excitation is from T2 to E. This transition is a forbidden one, since it occurs between levels of the d-sheU. Therefore the parity does not changed. The parity selection rule may be relaxed by the coupling of the electronic transition with vibrations of suitable symmetry. 

By reference to the MO scheme in Fig. 2, the bands at X < 400 nm have been assigned to sharp and intense parity-allowed transitions between occupied (bonding) and empty (antibonding) MOs. Such excitations include Au(HOMO)— fJg(LUMO + 1) and hg—> Optical transitions between the HOMO(Au) and LUMO(f/u), which are electric dipole forbidden, occur via excitation of a vibronic state with appropriate parity symmetry and account for the broad and low intensity band at X > 400 nm. 

Example 10.2-2 The ground-state configuration of an net octahedral complex is l2g, and the first excited configuration is el so that optical transitions between these two configurations are symmetry-forbidden by the parity selection rule. Nevertheless, Ti(H20)g3 shows an absorption band in solution with a maximum at about 20 000 cm-1 and a marked shoulder on the low-energy side of the maximum at about 17 000 cm Explain the source and the structure of this absorption band. 

There is, however, a fundamental difference that makes optical selectivity based on ex far more important than the electrochemical selectivity derived from the applied potential. In electrochemistry, at a given applied potential, all electrochemical reactions that have equal or lower energy will take place. This means that the selectivity defined by the choice of the electrode potential only is very limited. In contrast, optical transitions are resonant and fall off on both sides of the absorption maximum. If not enough energy is applied, or if too much energy is applied, the transition (and therefore the interaction) is forbidden that is, its probability is low. 

When a diatomic molecule dissociates photochemically it yields atoms either in their ground or in excited states. When the optical transition leading to dissociation is not forbidden, and does not arise from predissociation, one of the two atoms formed will not be in its ground state. 

This apparently is based on the assumption that the cross-section depends on exp (-AEjkT). However, Frish and Bochkova141 claim to have demonstrated that the 8P state is produced only in very low yield. They observed the emission from excited sodium atoms in an electric discharge in He, Hg and Na mixtures at very low total pressures. Their data appear to show that the cross-section for excitation of the 8P state, the process with the smallest energy discrepancy and for which optical transitions of both atoms are allowed, is smaller than the cross-section into the 9S state, which is optically forbidden for the sodium. 

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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