Relaxation of selection rules

In solids, the selection rules can seldom he considered as absolute rules. The situation is reminiscent of towns with low traffic morals when the traffic light is green everyone crosses (allowed transition, no selection rules), at red there are still a few people who cross against the rules (forbidden transition, but selection rule slightly relaxed). The relaxation of selection rules is connected to wavefunction admixtures into the original, unperturbed wave functions. This can be due to several physical phenomena, like spin-orbit coupling, electron-vi brat ion coupling, uneven crystal-field terms, etc. Their treatment lies outside the scope of this book. The reader is referred to Refs. [11 and [3]. 

So far the effect of anharmonicity in determining the frequency of overtone (An >1) absorptions, and its effect in relaxing quantum selection rules to allow these transitions to have some absorption intensity have been considered. 

Relaxation of the rules can occur, especially since the selection rules apply strongly only to atoms that have pure Russell-Saunders (I-S) coupling. In heavy atoms such as lanthanides, the Russell-Saunders coupling is not entirely valid as there is the effect of the spin-orbit interactions, or so called j mixing, which will cause a breakdown of the spin selection rule. In lanthanides, the f-f transitions, which are parity-forbidden, can become weakly allowed as electric dipole transitions by admixture of configurations of opposite parity, for example d states, or charge transfer. These f-f transitions become parity-allowed in two-photon absorptions that are g g and u u. These even-parity transitions are forbidden for one photon but not for two photons, and vice versa for g u transitions [46],... 

We, therefore, anticipate that most of the vibrational excitation will be deposited in M rather than in O2 (formation of a strong M-02 complex might somewhat relax this selection rule ). Consequently, the variation of Fif with Ac will be almost entirely conditioned by variations in fm, the Franck-Condon factor for the molecule. Fortunately, semi-empirical formulas for evaluating fm have been developed (19, 24, 48), and one such expression is given in Equation 6. 

Another effect of anharmonicity is to relax the selection rules to give... 

The factor that most strongly influences allowedness of a transition is spin. Transitions between states with different spins, such as singlet and triplet, are very inefficient. Direct So to T1 absorption is rarely important, and the reverse emissive process, phosphorescence, occurs quite slowly. The heavy atom effect can relax this selection rule through a spin-orbit effect. As a result, S-T interconversions are much more facile in molecules that contain atoms such as Br or 1. The second major factor that influences the efficiency of transitions is the general spatial overlap of the wavefunctions for the two states. This term favors it,it transitions over ,ir transitions, for reasons discussed above. Another important factor is a general energy gap law. For processes such as intersystem crossing, the smaller the gap between the... 

Fluorescence lifetimes for strongly absorbing transitions in the visible are typically a few ns those for symmetry-forbidden fluorescence transitions, such as found with symmetrical polyaromatics can be hundreds of ns. Radiative lifetimes for phosphorescence, in the absence of any heavy-atom relaxation of the spin selection rule, can be as long as many minutes, while systems with some relaxation of the rule typically show phosphorescence radiative lifetimes of microseconds (qs) to milliseconds (ms). 

In principle the removal of the translational periodicity because of disorder relaxes the selection rules imposed by group theory and all phonons of the host lattice may become active. In principle, one can then expect to observe the activation of the whole density of states g( ) of the host lattice because of the perturbations by the end groups. The extent of... 

If the vibrational modes were strictly harmonic, no transitions involving changes in u, by more than 1 would be allowed. The effect of anharmonicity is to relax this selection rule (i.e., to allow bands caused by Au, > 1 to become allowed). Thus, overtone (Au, = 2,3,...) and combination (Au, = 1 Ay, = 1, where j represents a different mode) bands commonly appear weakly in the mid-infrared spectrum of organic compounds along with bands due to fundamental transitions (Au, = 1). 

The term following EL is always less than unity so that an adventitious correction to the laboratory energy occurs. This enhances the precision of the Er measurement. As with electrons, selection rules for ionization and dissociation seem to be relaxed. 

The transitions between energy levels in an AX spin system are shown in Fig. 1.44. There are four single-quantum transitions (these are the normal transitions A, A, Xi, and X2 in which changes in quantum number of 1 occur), one double-quantum transition 1% between the aa and j8 8 states involving a change in quantum number of 2, and a zero-quantum transition 1% between the a)3 and fia states in which no change in quantum number occurs. The double-quantum and zero-quantum transitions are not allowed as excitation processes under the quantum mechanical selection rules, but their involvement may be considered in relaxation processes. 

Thus the change in the direction of the spin angular momentum of the electron effectively imparts some singlet character to a triplet state and, conversely, triplet character to a singlet state. This relaxes the spin selection rule since J S St dr is no longer strictly zero. The greater the nuclear charge,... 

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