Particle-hole picture

While particle contractions connect an upper right with a lower left label (and are associated with a factor (1 — np)), hole contractions go from upper left to lower right, with a factor —np. Closed loops introduce another factor —LA graphical interpretation is possible, in agreement with that for the conventional particle-hole picture. We postpone this to the more general case of an arbitrary reference function (Section III.E). 

Note that a dot ( ) always means a matrix element of the antisymmetrized electron interaction g, a cross (x) a matrix element of the one-particle operator /, while an open square ( ) collects the free labels in any of these contractions. If the reference function is a single Slater determinant, all cumulants X vanish one is then left with particle and hole contractions, like in traditional MBPT in the particle-hole picture. 

The diagrams are interpreted in terms of the particle-hole formalism. The Fermi level is defined such that all single particle states lying below it are occupied and all above it are unoccupied. In the particle-hole picture, the reference state is taken to be a vacuum state, containing no holes below the Fermi level and no particles above it. Excitation leads to the creation of particle-hole pairs, with particles above the Fermi level and holes below it. 

Figure 3.2. Simple illustration of the particle-hole formalism. This figure shows the states given in the particle formalism in Figure 3.1 when depicted in the particle-hole picture, (a) shows the reference configuration or vacuum state with no particles above the Fermi level and no holes below it. (6) corresponds to a single excitation which creates a hole below the Fermi level and a particle above it. (c) is a doubly excited state with two holes and two particles and (d) is associated with a triply excited state with three holes and three particles. The particle-hole formalism focusses attention on the excitation process the particles and holes created during an excitation. The other electrons in the studied many-body system are merely spectators to the excitation process.

At this point it is worth rephrasing some of the issues of the above discussions. The UPS spectra are a measure of the single-particle excitation spectrum of the molecule, in so far as removal of an electron is concerned, while UAS data are a measure of the particle-hole excitation spectrum. In other terms, UPS measures the molecular-ion states while UAS measures excited states of the neutral molecule. For a molecule in isolation, in a one-electron picture the valence electron molecular cation states are comprised of the set of one-electron molecular orbitals (mo s) containing one half-filled (usually non-degenerate) molecular orbital and the totality of other fully occupied orbitals, distorted from their situation in the neutral molecule due to the removal of an electron from the molecule in a photoelectron... 

Excitons are the simplest manifestations of many-body elementary excitations in crystalline solids. These are the bound states of an electron-hole system held by a Coulomb attraction - not as strong as in a hydrogen atom but more like in positronium. The ground and excited states of an exciton are properly represented only in a two-particle band picture (Fig. 1) [1]. The process of creation, stabilization and recombination of excitons could well be conveniently investigated through ambient optical absorption and photoluminescence in I-VII compounds. 

Goldstone used a second quantized particle-hole formalism based on an arbitrary choice of vacuum state. The interaction representation, which is intermediate between the Schrddinger and Heisenberg pictures, was employed and the energy was evaluated by the Gell-Mann-Low formalism78 with Hamiltonian... 

So far we have used the picture of operators like H and p, acting on states like l rs) and Q/) in the Hilbert space Y. For developing perturbation theoretic expansions, however, it is useful to use the complementary concept of super-operators acting on Fock-space operators as defined in Sec. IIC. Using the super-operator H, the definition for the extended particle-hole Green s function of Eq. (23) can be written as... 

The fifth rung of Jacob s ladder adds exact correlation as new ingredient. One might think of this as an expansion of the density space of a system by adding virtual densities into the picture. One approach to this problem is the use of the random phase approximation (RPA). RPA in DFT in turn is closely related to time-dependent DFT (TD-DFT). The essence of RPA might be described as constructing the excited states of a system as a superposition of particle-hole excitations. 

The experiment conducted by Rutherford and his co-workers involved bombarding gold foil with alpha particles, which are doubly charged helium atoms. The apparatus used in their experiment is shown in Figure 14-9. The alpha particles are produced by the radioactive decay of radium, and a narrow beam of these particles emerges from a deep hole in a block of lead. The beam of particles is directed at a thin metal foil, approximately 10,000 atoms thick. The alpha particles are delected by the light they produce when they collide with scintilltaion screens, which are zinc sulfide-covered plates much like the front of the picture tube in a television set. The screen... 

At present there is a sufficiently complete picture of photoelectrochemical behavior of the most important semiconductor materials. This is not, however, the only merit of photoelectrochemistry of semiconductors. First, photoelectrochemistry of semiconductors has stimulated the study of photoprocesses on materials, which are not conventional for electrochemistry, namely on insulators (Mehl and Hale, 1967 Gerischer and Willig, 1976). The basic concepts and mathematical formalism of electrochemistry and photoelectrochemistry of semiconductors have successfully been used in this study. Second, photoelectrochemistry of semiconductors has provided possibilities, unique in certain cases, of studying thermodynamic and kinetic characteristics of photoexcited particles in the solution and electrode, and also processes of electron transfer with these particles involved. (Note that the processes of quenching of photoexcited reactants often prevent from the performing of such investigations on metal electrodes.) The study of photo-electrochemical processes under the excitation of the electron-hole ensemble of a semiconductor permits the direct experimental verification of the applicability of the Fermi quasilevel concept to the description of electron transitions at an interface. 

A quite simple picture is obtained in the ET case if we go from many-particle theory to orbitals via Koopmans theorem. This treatment is correct in the limit case when donor and acceptor exchange electrons using well-separated MO s on donor and acceptor. The simplest example is the case studied by McConnell [7] (fig.l). Two identical n systems are connected via a hydrocarbon chain, which acts as a bridge. ET is possible in an open shell system. We may assume that either the whole ET system is either a negative ion or a positive ion and that the corresponding neutral molecule has closed shells. In the former case the electron occupies 7t LUMO. In the latter case there is a hole in rt HOMO. 

Self-Energy and Spectral Function for a Core Hole. The Quasi-Particle Picture... 

Recently, Connerade59 has pointed out this and other cases of level crossing and given experimental evidence for the breakdown of the quasi-particle picture for a 4 d-core hole in In. The situation is complicated by the fact that the experiment concerns 4d-threshold photoabsorption and therefore involves the participation of a bound or very slow photoelectron which perturbs the picture of an interacting core hole. One therefore has to consider interactions between discrete nd continuous single and double excitations. 

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