Self-energy proper

The aim of this work is to demonstrate that the above-mentioned unusual properties of cuprates can be interpreted in the framework of the t-J model of a Cu-O plane which is a common structure element of these crystals. The model was shown to describe correctly the low-energy part of the spectrum of the realistic extended Hubbard model [4], To take proper account of strong electron correlations inherent in moderately doped cuprate perovskites the description in terms of Hubbard operators and Mori s projection operator technique [5] are used. The self-energy equations for hole and spin Green s functions obtained in this approach are self-consistently solved for the ranges of hole concentrations 0 < x < 0.16 and temperatures 2 K< T <1200 K. Lattices with 20x20 sites and larger are used. 

The decomposition of the irreducible part of the self-energy wave-function correction term is depicted in Fig. 2. The divergent terms are these with zero and one interaction in the binding potential present, below referred to as zero-potential term and one-potential term , respectively. The charge divergences cancel between both terms. In addition, a mass counter term dm has to be subtracted to obtain proper mass renormalization similar to the case of the free self energy [47] (for our schemes see also [44]). The zero- and one-potential... 

Other ions in the solution. The self-energy of a dipole embedded in a dielectric sphere is the key to Onsager s theory of the dielectric constant of dipolar fluids. Equally, in any theory for, say, the surface energy of water, or adsorption of molecule, the self-energy of a molecule as a function of its distance from an interface is involved. In adsorption proper, the same selfenergy for a molecule appears in the partition function of statistical mechaiucs from which the adsorption isotherm is derived. 

In equations (58), (59), and (60), the indices 1-3 distinguish between the different spatial coordinates of integration. For evaluation of these formulae and proper handling of divergencies we refer to [83], For the hyperfine splitting in hydrogenlike ° Bi, we obtain a self energy contribution of -0.06144(1) eV. 

This equation is the main result of the present considerations. In order to define the two-particle self energy (w) and for establishing the connection to the familiar form of Dyson s equation we adopt a perturbation theoretical view where a convenient single-particle description (e. g. the Hartree-Fock approximation) defines the zeroth order. We will see later that the coupling blocks and vanish in a single-particle approximation. Consequently the extended Green s function is the proper resolvent of the zeroth order primary block which can be understood as an operator in the physical two-particle space ... 

Fig. 9 Graphical representation of the Dyson equation for the two-particle Green s function. The crossed box represents the proper or irreducible two-particle self energy...

Fig. 5. Graphs contributing to the improper and proper self-energy, respectively, derived from the graphs in Fig. 1.

Because many effective pairwise additive potentials do not include the self-energy of the dipoles in their original parameterizations, their reported enthalpy values require corrections to make a proper comparison with experi-... 

Nor is the methodology exhaustive in terms of experimental data, as required of a proper alloy theory. Indeed, it produces results that are known to be contrary to the behavior of physical systems. For example, it yield a self-energy that is real whereas the dispersion in the experimental spectra of disordered alloys suggests a complex quantity. Because the method lacks scientific foundation, its generalization to incorporate a broader spectrum of physical reality is unjustified. 

There seems to be no way of alleviating this fundamental problem. It is the problem that must be overcome in order to allow for a unified treatment within real and reciprocal space. The CPA and the MCPA do allow such a treatment but neither of them yields a properly k-dependent self-energy. In all other cases, particularly in connection with attempts to preserve lattice periodicity, the discrepancies with respect to scattering theory provide a formidable stumbling block to their development. 

Phosphors usually contain activator ions in addition to the host material. These ions are dehberately added in the proper proportion during the synthesis. The activators and their surrounding ions form the active optical centers. Table 1 Hsts some commonly used activator ions. Some soflds, made up of complexes such as calcium tungstate [7790-75-2] CaWO, are self-activated. Also in many photolurninescence phosphors, the primary activator does not efficiently absorb the exciting radiation and a second impurity ion is introduced known as the sensitizer. The sensitizer, which is an activator ion itself, absorbs the exciting radiation and transfers this energy to the primary activator. 

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