Radiative ‘allowed’ transitions

The selection rules for radiationless transitions are just the opposite of those for radiative transitions. The nuclear kinetic operator is symmetric. The symmetric aromatic molecules normally have symmetrical ground state and antisymmetrical excited state. Therefore, allowed transitions are ... 

The selection rules for radiationless transitions are just the opposite of those for radiative transitions. Allowed transitions are ... 

Specifically, the collision-induced absorption and emission coefficients for electric-dipole forbidden atomic transitions were calculated for weak radiation fields and photon energies Ha> near the atomic transition frequencies, utilizing the concepts and methods of the traditional theory of line shapes for dipole-allowed transitions. The example of the S-D transition induced by a spherically symmetric perturber (e.g., a rare gas atom) is treated in detail and compared with measurements. The case of the radiative collision, i.e., a collision in which both colliding atoms change their state, was also considered. 

The lifetimes of molecules which undergo allowed transitions in the ultraviolet have radiative lifetimes of the order of 10 8 to 10" 9 sec. If the transition is orbitally forbidden, the radiative lifetime of the excited state is 10"5. 

SELECTION RLILES (Energy Levels). It was found early in the. study of atomic spectra that radiative transitions between certain pairs of energy levels seldom or never occur. A set of rules which are expressed in terms of the differences of the quantum numbers of the two states involved allow a prediction of allowed transitions and forbidden transitions. The conditions for allowed transitions are ... 

The results of experimental research have also stimulated the appearance of theoretical papers devoted to the analysis of an elementary act of electron tunneling reactions in terms of the theory of non-radiative electron transitions in condensed media. It has been shown that this theory allows one to explain virtually all the known experimental data on electron tunneling reactions. 

Obviously, the various electronically excited states of an atomic or molecular ion vary in their respective radiative lifetime, t. The probability distribution applicable to formation of such states is thus a function of the time that elapses following ionization. Ions in metastable states, which have no allowed transitions to the ground state, are most likely to contribute to ion-neutral interactions observed under any experimental conditions since these states have the longest lifetimes. In addition, the experimental time scale of a particular experiment may favor some states over others. In single-source experiments, short-lived excited states may be of greater relative importance than in ion-beam experiments, in which there is typically a time interval of a few microseconds between ion formation and the collision of that ion with a neutral species, so that most of the short-lived states will have decayed before collision. There are several recent compilations of lifetimes of excited ionic states.lh,20 ,2,... 

First approximation theory leads to certain wave mechanical selection rules on the basis of which a radiative electronic transition may be classified as allowed (high probability) or forbidden (vanishingly low probability). Some forbidden transitions are indeed too weak to observe easily but in actual practice with polyatomic molecules the selection rules often break down sufficiently to permit reasonably strong absorption processes to occur. The following kinds of transition are forbidden... 

To sum up, we have developed a general non-perturbative method that allows one to calculate the rate of relaxation processes in conditions when perturbation theory is not applicable. Theories describing non-radiative electronic transitions and multiphonon relaxation of a local mode, caused by a high-order anharmonic interaction have been developed on the basis of this method. In the weak coupling limit the obtained results agree with the predictions of the standard perturbation theory. 

Figure 19 Jablonski diagram (schematic) showing the energetic location of the first excited singlet Si and triplet states Ti with respect to the electronic singlet ground state So and possible transitions between them. Radiative transitions are indicated by straight arrows, nonradiative processes by curly ones. Solid arrows represent spin-allowed transitions, dashed-dotted lines spin-forbidden ones.

For oxidized nc-Si there exist surface states at the Si/Si02 interface in which photogenerated electron-hole pairs can be localized when the optical band gap has increased enough in small crystallites (Figs 5a + 5b). From these states radiative recombination of the excitons can occur on a time scale of tens of microseconds. Ab initio calculations for one sided oxidized Si planar sheets show that there is a direct-allowed transition of 1.66 eV at the F point [7] In TTSS and PDS the sharp PL- and absorption bands together with the results from the microwave absorption indicate that the origin of the luminescence is of a molecular nature caused by localization in the Si backbone Those mplecular systems, small clusters, nanocrystallites or strongly confined artificial systems may have a potential for a fully Si-based optoelectronic in the future. 

Second, the dependence on a> is a very significant property of the radiative decay rates. Assmning similar transition dipoles for allowed transitions, Eq. (3.31) predicts that lifetimes of electronically excited states (2i of order lO cm ) are shorter by a factor of -lO than those of vibrational excitations (<021 of order 10 cm ), while the latter are 10 shorter than those of rotational excitations (ct>2i of order lO cm ), as indeed observed. 

In the case of the octahedral uranate group, the u -> g transition is a magnetic-dipole allowed transition which becomes electric-dipole vibronically allowed by coupling with vibrations (c.f. Sect. 2.1). The radiative rate of a vibronic transition is temperature dependent (see e.g. Ref. 55). 

The macroscopical surface excitons obtained when retardation is taken into account, i.e. surface polaritons, cannot spontaneously transform into bulk emitted photons. Therefore, surface polaritons are sometimes said to have zero radiation width (it goes without saying that a plane boundary without defects it implies). At the same time the Coulomb surface excitons and polaritons in two-dimensional crystals possess, as was shown in Ch. 4, the radiation width T To(A/27ra)2, where A is the radiation wavelength, a is the lattice constant, and To the radiative width in an isolated molecule. For example, for A=500 nm and a = 0.5 nm the factor (A/2-7Ta)2 2x 104, which leads to enormous increase of the radiative width. For dipole allowed transitions To 5x10 " em, so that the value of T 10 cm-1 corresponds to picosecond lifetimes r = 2-kK/T x, 10 12s. 

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