Atomic spectroscopy notation

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 index number refers to the principal quantum number and corresponds to the K shell designation often used for the electron of the normal hydrogen atom. The principal quantum number 2 corresponds to the L shell, 3 to the M shell, and so on. The notation s (also p, cl, f to come later) has been carried over from the early days of atomic spectroscopy and was derived from descriptions of spectroscopic lines as sharp, principal, diffuse, and fundamental, which once were used to identify transitions from particular atomic states. 

It will be more useful in practice, however, to discuss the Russell-Saunders limit of weak spin-orbit coupling (15, 16). We shall show how to derive formulae applicable to atoms in spherical symmetry. Thus we shall change the notation to that used in atomic spectroscopy (15), writing S L Ms M ) for the ground state and l a S L Ms Ml) for an ionised state. With spin-orbit coupling we must... 

The various options and search criteria are clearly listed in several introductory front pages and they are discussed in a general information section, where also other special features of the database are reviewed. In addition, this section includes a short compendium on atomic spectroscopy, which contains the basic physics, formulas and conversion factors in atomic spectroscopy, as well as a discussion of spectroscopic notations. 

Another way to see that we are dealing with a hole conduction process is to consider the ontermost electronic shell of the copper ions, which is called a 3d level in the notation of atomic spectroscopy. This level can hold a maximnm of 10 electrons, and is tilled for the ion Cn+. The ion Cn + has only nine electrons in its 3d level, which corresponds to 10 electrons pins one hole, and Cn + has 8 electrons, or 10 electrons pins two holes. Electrical cnrrent in the normal state is carried by these holes, which are in the condnction band, via the hopping mechanism of eqnation (21). Electric cnrrent in the supercondncting state is carried by Cooper pairs formed from these holes. 

In atomic spectroscopy, the notation S, P, D, F is employed to indicate terms with L values of 0, 1, 2, 3 respectively. The multiplicity is indicated by the number at the top as in 3P, for example. The spectral terms in an octahedral complex can be expressed in terms of only five ligand field quantum numbers which are written as A1( A, E, Tx and T2. The orbital degeneracies of these are 1, 1, 2, 3, 3 respectively. In discussing the absorption spectra of transition metal complexes, one should consider the number of terms into which each term of the free ion splits. The reason for this splitting is of course the differentiation of the degenerate d orbitals into two sets of orbitals. The S and P terms of the free ion are not split but transform as A1 and Tx respectively. The D terms are split into E and Ta while the F terms are split into Aj, Tj and T2 7. As in atomic spectroscopy, the multiplicity of each term is indicated by the number at the top, as for example 3T . 

The energy of electronic excitations is usually expressed employing the notation of atomic spectroscopy. In the case of a d " (n 0,10) transition metal ion in a crystalline matrix, local d—i d transitions can be employed to measure its allowed energy levels, and the crystal field acting on the metal site. 

Fig. 1. Energy levels of trivaient lanthanides below 43000 cm (5.3 eV) arranged according to the number q of 4f electrons. Excited levels known frequently to luminesce are indicated by a black triangle. The excited levels corresponding to hypersensitive transitions from the ground state are marked with a square. For each lanthanide, J is given to the right (in the notation of atomic spectroscopy, ] is added to the Russell-Saunders terms as lower-right subscripts). When the quantum numbers S and L are reasonably well-defined, the terms are indicated to the left. It may be noted that the assignments and F< in thulium(lll) previously were inverted these two levels with 7 = 4 actually have above 60% of H and F character, respectively. Calculated 7-levels are shown as dotted lines. They are taken from Carnall et al. (1968) who also contributed decisively to the identification of numerous observed levels, mainly by using the Judd-Ofelt parametrization of band intensities.

A combination of laser-induced fluorescence with classical absorption and emission spectroscopy has yielded a wealth of data on the excited electronic states of CeO. However, as noted by Linton et al., the spectroscopic data of upper states is less complete and are shown in table 54. Linton et al. (1983a, b) used empirical notation taken from atomic spectroscopy to designate these states. 

Based largely upon spectroscopic measurements (i.e., the observation of quantized absorption and emission of energy—as in atomic spectroscopy, about which you may have already heard, and other forms of spectroscopy to be discussed in Chapter 2) and the utility of the concept in making successful predictions, we define as an orbital that particular volume in space, near a nucleus, in which there is a high probability of finding an electron associated with that nucleus. By the Pauli exclusion principle, no more than two electrons can occupy a given orbital and if there are two electrons in the orbital, they must differ with regard to a property called spin. This property has only two possible values, frequently symbolized by the notations t and i (or sometimes by +V2 and -Vi, respectively), and if two electrons have the same values (i.e., tt or x(i) for this property, they are said to be unpaired and they cannot occupy the same orbital. Only paired (Ti) electrons can occupy the same orbital. 

Table Al.l Electronic configuration of the elements. Elements in square brackets (e.g., [He]) imply that the electronic configurations of the inner orbitals are identical to those of the element in brackets. Thus silver (Ag, atomic number 47) has a configuration of [Kr]4(7105 1, which if written out in full would be s22s22p62s22p62d1QAs1Ap6Adw5>s1, giving 47 electrons in all. For the heavier elements (atomic number above 55), the alternative notation K, L, M is used to denote the inner shells corresponding to orbitals 1, 2 and 3 respectively. This notation is common in X-ray spectroscopy (see p. 33). (Adapted from Lide, 1990.)...

In the development of the concepts of atomic structure much of the experimental evidence came from optical and x-ray spectroscopy, From this work certain notations have arisen that are now an accepted part of the language. For example, the n = I shell is sometimes known as the K-shell, the n 2 shell as the L-shell. the it = 3 shell as the JM-shell. etc., with consecutively following letters of the alphabet being used to designate those shells with successively higher principal quantum numbers. A Roman numeral subscript further subdivides the shells in accordance with the n, J, and j quantum numbers of the electrons, as shown in Table 4,... 

Notation N, coordination number R, distance between absorber and backscatterer atom A a2, Debye-Waller factor AEo, inner potential correction. Commonly accepted error bounds on structural parameters obtained by EXAFS spectroscopy are N, 10-15% R, 0.02 A ... 

The value of performing intermultiplet spectroscopy has been demonstrated by optical results on ionic systems. Well defined atomic spectra from intra-4f transitions have been measured up to 6 eV in all the trivalent lanthanides (except, of course, promethium) [Dieke (1968), Morrison and Leavitt (1982) see fig. 1 based on Carnall et al. (1989)]. Each level is characterised by the quantum numbers L, S, J, F), where L and 5 are the combined orbital and spin angular momenta of the 4f electrons participating in the many-electron wavefunctions, and J is the vector sum of L and 5. The quantum number F represents the other labels needed to specify the level fully. It is usually the label of an irreducible representation of the crystal field and we shall omit it. The Coulomb potential is responsible for separating the 4f states into Russell-Saunders terms of specific L and S, while the spin-orbit interaction is diagonal in J and so splits these terms into either 25-1-1 or 2L -I-1 levels with 7 = L - 5 to L -f 5. Provided the spin-orbit interaction is weaker than the Coulomb interaction, as is the case in the lanthanides, the resulting levels consist of relatively pure L, 5, J), or in spectroscopic notation states. These 27-1-1 manifolds are then weakly... 

Note the ground-state atomic term symbol for Cr is F, which splits into T2, Ti and A2 for an octahedral transition metal complex. For more information regarding term symbol notation and absorption spectra for transition metal complexes, see Shiiver et al. Inorganic Chemistry, 4th ed., W. H. Freeman New York, 2006. http //www.scribd.com/doc/6672586/Electronic-Spectroscopy-l Note excited electrons give off their energy via infrared emission and thermal interactions with the corundum crystal lattice, referred to as electron-phonon (lattice vibrations) interactions. 

Complete introductions to the chemistry and to the structural diversity of CBHs, glycoconjugates, and glycans can be found in the literature [2, 3, 28]. Here we present only the basic properties of mono- and oligosaccharides relevant for gas-phase spectroscopy and necessary to follow the discussions which follow. We begin by introducing the main actors of this chapter, their naming, atomic numbering, and conformational notation. 

In Summary Determination of organic structures relies on the use of several experimental techniques, including elemental analysis and various forms of spectroscopy. Molecular models are useful aids for the visualization of the spatial arrangements of the atoms in structures. Condensed and bond-line notations are useful shorthand approaches to drawing two-dimensional representations of molecules, whereas hashed-wedged fine formulas provide a means of depicting the atoms and bonds in three dimensions. 

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