Excitons selection rules

The arrangement of the individual transition dipoles in an aggregrate or polymer determines the selection rule for exciton transitions. Several possible dipole arrangements are shown in Figure 6.6... 

Photoluminescence of ZnS Mn occurs when the phosphor absorbs photon energy corresponding to the band gap of ZnS and relaxes to release the excess energy of the exciton (a pair of an s-p electron and a hole). Based on the selection rule of Laporte, the symmetrical field of 6-coordinated Mn(ll) does not allow the d-d transition since it is not associated with the change in the parity. The 4-coordinated Mn(lI), in contrast, allows a partial d-p hybridization, enabling the d-d transition. 

Thus in either formulation the exciton spectrum consists of a series of bands, but the optical absorption spectrum consists of a series of lines because the selection rule... 

External Field. Examples are the interaction of a molecule in a solid with a phonon field83,156 or a migrating exciton.88,129,167 Both spin-free and point-group selection rules may turn out to be of some importance. (Radiative transitions are often treated in this formalism.)... 

D SELECTION RULES AND EXCITON COUPLING TO THE ELECTROMAGNETIC FIELD... 

The Kossel model (146) of single-electron transitions to unoccupied states has been applied to the interpretation of the absorption-edge structure of isolated atoms (inert gases) as well as to molecules and solids, in which case use is made of band-model calculations, including the possible existence of quasi-stationary bound states as exciton states. Parratt (229), who has carried out the first careful analysis of the absorption spectrum of an inert gas, assumed that dipole selection rules govern the transition possibilities, with allowed transitions being Is - np. 

Figure 2. Level schemes and selection rules for the ionized bound exciton transitions.

Figure 3. Level sehemes and selection rules for neutral bound exciton transitions.

In light of the above discnssion, the optical absorption spectrum of a quantum film is expected to consist of a series of steps, with the position of these steps corresponding to the transitions between heavy or light hole quantum states and electron quantum states following the selection rule An = 0. Furthermore, since the widths of the wells are commonly smaller than the calculated diameter of an exciton, the exciton binding... 

Although some optical techniques, such as soft X-ray absorption and optical reflectance measurements, provide comparative information about solids with higher energy resolution, EELS enjoys several unique advantages over optical spectroscopies. First of all, unlike optical reflectance measurements which are sensitive to the surface condition of the sample, the transmitted EELS represents the bulk properties of the material. Secondly, EELS spectra can be measured with q along specific controllable directions and thus, can be used to study the dispersion of plasmons, excitons, and other excitations [8.1-8.5]. Such experiments offer both dynamics as well as symmetry information about the electronic excitations in solids. In addition, the capability to probe the electronic structure at finite momentum-transfer also allows one to investigate the excited monopole or quadrupole transitions, which cannot be directly observed by conventional optical techniques limited by the dipole selection rule. 

This example shows clearly that the emission process is very different from the (simple) absorption process. For all details the reader is referred to the literature [SJ. Finally we draw attention to the fact that the life time of the relaxed self-trapped exciton in the alkali halides is longer 10 s) than expected for an allowed transition (I0 - I0 "s). This is ascribed to the fact that the emitting state contains an amount of spin triplet character. Such a triplet state arises when the spins of the electron and the hole are oriented parallel. The emission transition becomes (partly) forbidden by the spin selection rule (see Chapter 2). 

To explain the held dependence, we have to assume that the applied held has an influence on v hether the spin selection rules can be obeyed in the fusion process. A kinetic explanation by Merrifleld and Johnson [49, 50] assumes in the reaction Ti + Ti (Ti Ti) Si + So the existence of an intermediate pair state (Ti Ti), in v hich the tv o excitons repeatedly collide before they react. The possible spin correlations in this pair state have both triplet as well as singlet character. The triplet fraction in the pair state is also influenced by an applied magnetic field via the Zeeman interaction of the coupled individual spins with the field. The strength and direction of the field thus determine the relative fraction of triplet and singlet states in the pair. The singlet fraction leads to the states Si and So, and thus to delayed emission. Therefore, the intensity and lifetime of the emission can be modulated by an applied magnetic field. This holds for all biexcitonic processes in which two triplet states participate. 

Due to the spin selection rule, photon absorption can only generate singlet excitons. However, the ISC induced by internal magnetic interaction (from hyperfine coupling or SOC) can convert singlets into triplets in excitonic states (Scheme 4.3). 

Fig. 9.13. Electronic selection rules determine that intermolecular interconversion occurs from the n = 1, j = 1 intermolecular exciton to the n = 1, j = 1 intramolecular exciton.

We note that the effective-particle description is still valid when there is selftrapping. In this case the centre-of-mass wavefuctions are not the particle-in-the-box wavefunctions appropriate for a linear chains (eqn (9.130)), but they are the ortho-normalized functions appropriate for the particular potential well trapping the effective particle. The key point is that because these are ortho-normalized functions and because the potential wells for the excitons and polarons are very similar the selection rules for interconversion are still valid. Thus, interconversion occurs between a pair of states with the same center-of-mass quantum numbers. 

Nuclear excitation and nuclear resonant scattering with synchrotron radiation have opened new fields in Mossbauer spectroscopy and have quite different aspects with the spectroscopy using a radioactive source. For example, as shown in Fig. 1.10, when the high brilliant radiation pulse passed through the resonant material and excite collectively the assemblies of the resonance nuclei in time shorter than the lifetime of the nuclear excited state, the nuclear excitons are formed and their coherent radiation decay occurs within much shorter period compared with an usual spontaneous emission with natural lifetime. This is called as speed-up of the nuclear de-excitation. The other de-excitations of the nuclei through the incoherent channels like electron emission by internal conversion process are suppressed. Synchrotron radiation is linearly polarized and the excitation and the de-excitation of the nuclear levels obey to the selection rule of magnetic dipole (Ml) transition for the Fe resonance. As shown in Fig. 1.10, the coherent de-excitation of nuclear levels creates a quantum beat Q given by... 

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