INDEX selection rules

Perhaps the most notable aspect of the history of the API operation is that it has been shaped at every step by those who use the system. Created by information speciaHsts within the petroleum iadustry, it has beea governed by a technical information committee made up of company representatives, and guided by a series of iadustry task forces, which have modified as aeeded the indexing thesaums, subject selectioa guideliaes, and selection rules for countries ia pateat coverage, journals, and other sources ia the aoapateatHterature. 

The number of multipole parameters is reduced by the requirements of symmetry. As discussed in chapter 3, the only allowed multipolar functions are those having the symmetry of the site, which are invariant under the local symmetry operations. For example, only / = even multipoles can have nonzero populations on a centrosymmetric site, while for sites with axial symmetry the dipoles must be oriented along the symmetry axis. For a highly symmetric site having 6 mm symmetry, the lowest allowed / 0 is d66+ all lower multipoles being forbidden by the symmetry. The index-picking rules listed in appendix D give the information required for selection of the allowed parameters. 

Fourier transform infrared microscopes are equipped with a reflection capability that can be used under these circumstances. External reflection spectroscopy (ERS) requires a flat, reflective surface, and the results are sensitive to the polarization of the incident beam as well as the angle of incidence. Additionally, the orientations of the electric dipoles in the films are important to the selection rules and the intensities of the reflected beam. In reflectance measurements, the spectra are a function of the dispersion in the refractive index and the spectra obtained are completely different from that obtained through a transmission measurement that is strongly influenced by the absorption index, k. However, a complex refractive index, n + ik can be determined through a well-known mathematical route, namely, the Kramers-Kronig analysis. 

For textured samples under stress two sample symmetries must be distinguished texture and strain/stress sample symmetry. Sometimes they are identical, but generally the strain/stress sample symmetry is lower. A simple example is offered by Equation (107). The texture has a spherical symmetry but the strain sample symmetry is in general triclinic. The texture sample symmetry must form a super group of the strain sample symmetry because Ph(y) must be invariant to both sample symmetries. Concerning the selection rules imposed by the sample symmetry, one expects them to be identical to those for the texture of the same sample symmetry. Indeed, the invariance conditions act directly on Equation (121) and (122) that are identical to Equations (38) and (39). Hence, the selection rules in the index n for the coefficients a , /I , y and 2" are those from the Table 12.3. 

In this mechanism, two-photon transitions are forbidden and the excitation of the participating molecules occurs through one- and three-photon allowed transitions. Both the real (laser) photons are absorbed by one molecule, excitation of its partner resulting from the virtual photon coupling. Because of the difference in selection rules from the previous case, the first two terms of Eq. (5.13) are now zero, and contributions arise only from the third and fourth terms. It must also be noted that setting the two absorbed photon frequencies to be equal in Eq. (5.16) to produce zJy, (co,o>) introduces index symmetry into the tensor, as indicated by the brackets embracing the first two indices. A factor of j must then be introduced into the definition of this tensor in order to avoid over-counting contributions. The transition matrix... 

The symmetry of an isolated atom is that of the full rotation group R+ (3), whose irreducible representations (IRs) are D where j is an integer or half an odd integer. An application of the fundamental matrix element theorem [22] tells that the matrix element (5.1) is non-zero only if the IR DW of Wi is included in the direct product x of the IRs of ra and < f. The components of the electric dipole transform like the components of a polar vector, under the IR l)(V) of R+(3). Thus, when the initial and final atomic states are characterized by angular momenta Ji and J2, respectively, the electric dipole matrix element (5.1) is non-zero only if D(Jl) is contained in Dx D(j 2 ) = D(J2+1) + T)(J2) + )(J2-i) for j2 > 1 This condition is met for = J2 + 1, J2, or J2 — 1. However, it can be seen that a transition between two states with the same value of J is allowed only for J 0 as DW x D= D( D(°) is the unit IR of R+(3)). For a hydrogen-like centre, when an atomic state is defined by an orbital quantum number , this can be reduced to the Laporte selection rule A = 1. This is of course formal, as it will be shown that an impurity state is the weighted sum of different atomic-like states with different values of but with the same parity P = ( —1) These states are represented by an atomic spectroscopy notation, with lower case letters for the values of (0, 1, 2, 3, 4, 5, etc. correspond to s, p, d, f, g, h, etc.). The impurity states with P = 1 and -1 are called even- and odd-parity states, respectively. For the one-valley EM donor states, this quasi-atomic selection rule determines that the parity-allowed transitions from Is states are towards np (n > 2), n/ (n > 4), nh (n > 6), or nj (n > 8) states. For the acceptor states in cubic semiconductors, the even- and odd-parity states labelled by the double IRs T of Oh or Td are indexed by + or respectively, and the parity-allowed transition take place between Ti+ and... 

The existence of the doublet systems in the alkali metal elements requires another quantum number. This number was called the inner quantum number by Sommerfeld and is designated by the letter J and is used to distinguish the components of doublets. The S terms all have a J index of the P terms of and I and the D terms of f and f. Table 2-2 lists the J values for doublet terms. Analysis of the spectra of the alkali metals leads to the selection rule that AJ = 0 or 1, but also that the transition from J = 0 to J = 0 is excluded. 

Nonmetallic inorganic materials are widely used for optical purposes lenses, pigments, interference filters, laser hosts, luminescent coatings, displays, solar cells, fiber optics, lamp bulbs, and tubes. For optical applications use is made of the refractory index, light absorption, luminescence, and nonlinear optical behavior of materials. These are intrinsic but may depend on the concentration of impurities. Refraction index and optical absorptivity in insulators are atomic properties and are only indirectly related to the structure, but the structure affects the selection rules and the term splitting in the atomic chromophores. The coordination number determines the intensity and wavelength of absorption and... 

Several topics are not indexed here (e.g. Group Theory, selection rules, polarizability, symmetry, bond lengths, bimodal behavior, exsolution, zonation, extraction of thermodynamic data), but they appear in various abstracts indexed under another keyword. 

In the harmonic oscillator approximation the vibration of polyatomic molecules is that of normal modes, each acting like an independent harmonic oscillator. We number the normal modes with an index i, ranging from 1 to 3n — 5 for linear molecules and ranging from 1 to 3n — 6 for nonlinear molecules. The selection rules for vibrational tfansitions are ... 

Characteristic X-ray emission spectra consist of spectral series (K, L, M, N...), whose lines have a common initial state with the vacancy in the inner level. Labels of basic X-ray transitions are shown in Figure 2. All electron levels with the principal quantum number n equal to 1,2, 3, 4, etc. are named as K, L, M, N etc. levels and denoted with corresponding Greek letters and digit indexes. The electron transitions which satisfy the dipole selection rules... 

Appendix IV Chemical Substance Index Names (rules for the selection of systematic CA Index Names). 

Selection of a name for a specific compound is heavily influenced by the purpose at hand communication to a general audience, communication with specialists, or storage/retrieval through archival indexes. The first requires the simplest rules possible the second requires the shortest names possible and the third requires rigid adherence to a set of rules that will reliably generate a unique name. The name chosen may be different for each situation, although that is not necessarily so. 

Owing to possible future restrictions that could preclude the testing of samples with all five toxicity tests, we evaluated the index response with a reduced battery of toxicity tests. The basic rule for the selection of tests in a reduced battery was to maintain one primary producer, one primary consumer and a secondary consumer. The test combinations of two selected reduced batteries were Hydra, Daphnia and Lactuca tests (H-D-L) and Hydra, Daphnia and S. capricornutum (H-D-S) tests... 

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