In optical transitions

The Stark effect is electric-field-induced change in optical transition energy of materials, and the effect is observed as spectral change in absorption due to the energy shift. In the linear Stark effect, energy shift of optical transition Av in proportion to the electric field F is presented by... 

Because many physical systems possess certain types of symmetry, its adaptation has become an important issue in theoretical studies of molecules. For example, symmetry facilitates the assignment of energy levels and determines selection rules in optical transitions. In direct diagonalization, symmetry adaptation, often performed on a symmetrized basis, significantly reduces the numerical costs in diagonalizing the Hamiltonian matrix because the resulting block-diagonal structure of the Hamiltonian matrix allows for the separate... 

Figure 1. Relation of line width, transition energy, and recoil energy, (a) Overlap (schematic) of emission and absorption lines in optical transitions, (b) Absence of overlap (schematic) of emission and absorption lines in nuclear transitions involving atoms free to recoil. Drawn to scale, separation between two lines would be about 4 X 10 the width of each line at half rriaximum...

The principal selection rule is provided as in optical transitions, by the momentum conservation condition ... 

The coefficients accounting for the conservation of the angular momentum in optical transitions are of the form [36, 39, 153]... 

The nature of the initially prepared state is of paramount importance in determining (1) the subsequent IVR dynamics of a species and (2) the way in which the dynamics is manifest in time-resolved and time-integrated fluorescence. The theoretical picture, reviewed in Section III B of the manifestations of IVR in time-resolved fluorescence relies on the assumption that single zero-order states act as doorway states in optical transitions from and to... 

Shakeup represents a fundamental many-body effect that takes place in optical transitions in many-electron systems. In such systems, an absorption or emission of light is accompanied by electronic excitations in the final state of the transition. The most notable shakeup effect is the Anderson orthogonality catastrophe [5] in the electron gas when the initial and final states of the transition have very small overlap due to the readjustment of the Fermi sea electrons in order to screen the Coulomb potential of pho-toexcited core hole. Shakeup is especially efficient when the optical hole is immobilized, and therefore it was widely studied in conjunction with the Fermi edge singularity (FES) in metals [6-8] and doped semiconductor quantum wells [9-15]. Comprehensive reviews of FES and related issues can be found in Refs. [16,17]. 

J.J. Forney, A. Quattropani, F. Bassani, Choice of gauge in optical transitions, Nuove Cimento B 37 (1977) 78. 

J. Bergou, Gauge invariance and gauge independence in optical transitions, J. Phys. B 16 (1983) L647. 

We are approaching the application of group theory in optical transitions in spectroscopy. The most important issue will be a decision whether an integral is zero or nonzero. If the integral is zero, then the transition is forbidden, while if it is nonzero, then it is allowed. To make such a decision, we have to use what is known as the direct product of irreducible representations. Imagine basis functions and that correspond to irreducible representations a and f of... 

Now only those are allowed in optical transitions (from the ground state Ag) that are labeled hy B3 . because only the direct product B3 x B3 may contain the fully symmetric irreducible representation Ag. Thus, the transitions Ag B3 as well as B3J, Ag are allowed, if the light is polarized along x i.e., perpendicularly to the ring of the molecule. 

Many Raman scattering Unes are observed for SiC, reflecting zone folding effects in phonon dispersion curves. These lines can be used to identify the polytype of SiC crystals, as mentioned in Sec. III.A. From the shift of the Raman peaks and the discrepancy of the selection rules in optical transitions, information about the internal stress and crystallinity of SiC crystals, respectively, can be obtained, as mentioned in Sec. ni.B. 

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