Intra-atomic transitions

Although the studies on OLEDs have achieved considerable success, it is still difficult to obtain pure emission colors from small organic molecules or conjugated polymers, because their emission spectra typically have a half peak width of about 100 nm. Lanthanide ions can exhibit spectrally narrow emission due to intra-atomic transitions within the 4f shell. Consequently, luminescent lanthanide complexes are good candidates as emitting materials in OLEDs. 

UPS from Adsorbate Core Levels.—As outlined above, an out-going photoelectron in its final state is a super-position of two coherent contributions a direct wave whose amplitude and symmetry are determined by the intra-atomic transition at the emitting site and an indirect wave generated by repeated scattering of the direct wave by the local atomic environment. It was suggested by Liebsch that this final-state scattering should lead to angular variations in the photoemission spectrum and would be examined best in core-level emission, which involves the simplest possible initial... 

We have discussed electronic transitions in insulators resulting from oxygen valence band electrons either in the form of charge transfer into unoccupied metal states or as locahzed excitons. These transitions more or less scale with the width of the band gap. In transition metal oxides, on the other hand, localized intra-atomic transitions within the d manifold of electronic states are possible... 

The rate of this intramolecular isomerization depends on the chain length, with the maximum in the case of a six-atomic transition state, i.e., when the tertiary C—H bond is in the (3-position with respect to the peroxyl group [13]. For the values of rate constants of intramolecular attack on the tertiary and secondary C—H bond, see Table 2.9. The parameters of peroxyl radical reactivity in reactions of intra- and intermolecular hydrogen atom abstraction are compared and discussed in Chapter 6. 

To put it on a more quantitative basis, Johansson uses the expression for the critical point of the Mott transition as reformulated by Hubbard in terms of the bandwidth W[ and the polar state formation energy Uh (or effective intra-atomic correlation) (Eq. (36)). 

In Chap. E, photoelectron spectroscopic methods, in recent times more and more employed to the study of actinide solids, are reviewed. Results on metals and on oxides, which are representative of two types of bonds, the metallic and ionic, opposite with respect to the problem itineracy vs. localization of 5f states, are discussed. In metals photoemission gives a photographic picture of the Mott transition between Pu and Am. In oxides, the use of photoelectron spectroscopy (direct and inverse photoemission) permits a measurement of the intra-atomic Coulomb interaction energy Uh. 

However, the intra-atomic Coulomb interaction Uf.f affects the dynamics of f spin and f charge in different ways while the spin fluctuation propagator x(q, co) is enhanced by a factor (1 - U fX°(q, co)) which may exhibit a phase transition as Uy is increased, the charge fluctuation propagator C(q, co) is depressed by a factor (1 -H UffC°(q, co)) In the case of light actinide materials no evidence of charge fluctuation has been found. Most of the theoretical effort for the concentrated case (by opposition to the dilute one-impurity limit) has been done within the Fermi hquid theory Main practical results are a T term in electrical resistivity, scaled to order T/T f where T f is the characteristic spin fluctuation temperature (which is of the order - Tp/S where S is the Stoner enhancement factor (S = 1/1 — IN((iF)) and Tp A/ks is the Fermi temperature of the narrow band). 

Analysis of the valence-band spectrum of NiO helped to understand the electronic structure of transition-metal compounds. It is to be noted that th.e crystal-field theory cannot explain the features over the entire valence-band region of NiO. It therefore becomes necessary to explicitly take into account the ligand(02p)-metal (Ni3d) hybridization and the intra-atomic Coulomb interaction, 11, in order to satisfactorily explain the spectral features. This has been done by approximating bulk NiO by a cluster (NiOg) ". The ground-state wave function Tg of this cluster is given by,... 

Here U is the intra-atomic interaction defined in Chapter 4 and t, the hopping integral, is equal to B/2z, where B is the bandwidth and z is the coordination number. The suffixes i and j refer to the nearest-neighbour sites, and aia is the creation operator for site i. The suffix a refers to the spin direction. Hubbard found that a metal-insulator transition should occur when B/U = 1.15. Hubbard s analysis did not include long-range interactions, and therefore did not predict any discontinuity in the number of current carriers. 

Anderson type (though affected of course by long-range interaction). Until recently it was supposed by the present author that the former is the case. We must now favour, however, the latter assumption for many-valley materials (e.g. Si and Ge), the Hubbard gap opening up only for a value of the concentration n below nc. The first piece of evidence comes from a calculation of Bhatt and Rice (1981), who found that for many-valley materials this must be so. The second comes from the observations of Hirsch and Holcomb (1987) that compensation in Si P leads to localization for a smaller value of nc than in its absence. As pointed out by Mott (1988), a Mott transition occurs when B = U (B is the bandwidth, U the Hubbard intra-atomic interaction), while an Anderson transition should be found when B 2 V, where V is some disorder parameter. Since U e2/jcuH, where aH is the hydrogen radius, and K e2/jca, and since at the transition a 4aH, if the transition were of Mott type then it should be the other way round. 

As we have seen in Chapter 11, the energy levels of atoms and ions, depending on the relative role of various intra-atomic interactions, are classified with the quantum numbers of different coupling schemes (11.2)— (11.5) or their combinations. Therefore, when calculating electron transition quantities, the accuracy of the coupling scheme must be accounted for. The latter in some cases may be different for initial and final configurations. Then the selection rules for electronic transitions are also different. That is why in Part 6 we presented expressions for matrix elements of electric multipole (Ek) transitions for various coupling schemes. 

The presence of an outer open shell in an atom, even if this shell does not participate in the transitions under consideration, influences the X-ray radiation spectrum. Interaction of the vacancy with the open shell, particularly in the final state when the vacancy is not in a deep shell, splits the levels of the core. Depending on level widths and relative strength of various intra-atomic interactions, this multiplet splitting leads to broadening of diagram lines, their asymmetry, the occurrence of satellites, or splitting of the spectrum into large numbers of lines. 

These are electronic transitions between orbitals that are largely localised on different atoms. In coordination compounds ML where M is a d block element and L represents the ligands, we can distinguish two types of charge transfer L —> M and M — L. These are depicted schematically in Fig. 2.2, along with d-d transitions and intra-ligand transitions. 

X-ray fluorescence (XRF) and Auger electron (AES) yields as functions of the atomic number for K-shell vacancies. Auger transitions (solid curve) are more probable for lighter elements, while the X-ray yield (dashed curve) becomes dominant at higher atomic numbers. Similar plots can be obtained for L and M shell transitions. Intra-shell transitions are ignored in this analysis [81]. 

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