Anderson-Hamiltonian

A simple and widely used model to describe chemisorption is the Anderson model. The Anderson Hamiltonian (40) reads... 

Resonant processes dynamic solution of the Newns-Anderson Hamiltonian... 

In the next step, to analyze the resonant processes associated with charge exchange between He+ and He , we consider a spin-less Newns-Anderson Hamiltonian [18] where the level and the hopping terms Tis /a that have been neglected to calculate ElHe" "] and [He , are intioduced. This Hamiltonian reads... 

RESONANT PROCESSES DYNAMIC SOLUTION OF THE NEWNS-ANDERSON HAMILTONIAN... 

This case is analyzed using the H -levels and the H-Al interactions given in Fig. 6 and Table 1, respectively. As the H -level is always above the metal Fermi level, we can use semiclassical master equations for solving the Newns-Anderson Hamiltonian of this problem [21,22]. 

A similar effect arises when a half filled orbital overlaps a completely filled one. In this case, one has to consider the intermediate spin configuration of the ion which emits the electron. The metal-metal interaction is then introduced from the Anderson Hamiltonian [26] ... 

On the other hand, although spectra of Ce and Yb have been thus interpreted, no impurity model calculations of core- and outer-level spectra of Sm, Eu and Tm appear to have been reported so far. Indeed, the Anderson Hamiltonian is reputedly unsuitable for the interpretation of such systems. In the interesting cases of YbP [630] and YbA 3 [631], impurity model calculations have been performed by considering Yb as the hole-analogue of Ce. 

Surface recombination rate constant, Kr, at the interface is one of the most important factors that influence the overall rate, and this quantity depends mainly on the density of surface states, Dss E) and can be determined quantum mechanically, using the Anderson Hamiltonian formalism/ In this expression (76), cTc is the recombination cross section. The value of cTc can be obtained using the scattering theory. Sp E) is the velocity of photoexcited electron, and f E) represents the distribution of surface states which one may consider to be of Gaussian type of distribution, centered at the midgap energy. 

For —Sf A, U A and U + 2ef = 0 the Anderson Hamiltonian, eq.(1), can be transformed into the Coqblin-Schrieffer (CS) Hamiltonian. In this Kondo limit charge fluctuations are completely suppressed and the model describes an effective 4f-electron spin j which interacts via exchange with the conduction electrons... 

Anderson Hamiltonian (5.7.4) in terms of the Pauli matrices. This can be achieved using the Jordan-Wigner transformations [26] ... 

Having established the relationship between the parameters entering the Anderson Hamiltonian and high-energy excitations it is very instructive to illustrate the physical message delivered by this Hamiltonian within the simplest model which... 

In the following we examine models for a- and y-Ce which seek to explain the double structures observed in the 4f spectra. First, we consider satellite phenomena as they have been observed in a variety of systems, but then turn to the specific models which center around the Anderson Hamiltonian. Subsequent discussion examines other proposals. 

When the two-peaked structures were unambiguously observed for Ce and many of its compounds, several theoretical approaches were taken to explain their origin. Most of these studies of valence and 4f photoemission in Ce began with the assumption that the 4f state was best described as localized. Authors disagreed, however, not only on which terms were important in the Hamiltonian, but also on whether the double-peaked structure was present in the ground state or not. Many began with the Anderson Hamiltonian in which the 4f system is treated as an impurity on one site of the system (the origin) which can be written as... 

Allen and Martin (1982) and Lavagna et al. (1982, 1983) proposed that the y-a transition in Ce was related to the Kondo effect. Since Kondo systems have densities of states with two peaks, one very close to the Fermi level and one below, this offered a possible explanation of the two peaks in the photoelectron spectra, assuming that the photoabsorption process would transfer the structure in the density of states to the emitted spectrum. Detailed calculations of a photoelectron spectrum were not, however, carried out. The Kondo (or Abrikosov-Suhl) resonance in the density of states can be obtained from the Anderson Hamiltonian in the limit U CO (Lacroix 1981). For a Fermi level in the center of a valence band of width 2D and a constant density of states coupled by a constant matrix element V to an Nf-fold degenerate localized level at energy Sf below two peaks can arise in the density of states of the coupled system at low temperatures if is not too small. As... 

The essential point we wish to convey is that the Anderson Hamiltonian with one set of parameters ( f, U, and is capable of explaining the high energy ( 1 eV) excitation properties measured by XPS and BIS as well as the low energy ( 0.01eV) equilibrium properties in dilute and concentrated Ce and Yb materials. 

Gunnarsson and Schonhammer (1983a,b,c, 1985a,b see also chapter 64 in this volume) proposed a description of Ce spectroscopic data in terms of an Anderson impurity model, which allows to extract the crucial parameters, i.e., the 4f conduction band hybridization A and the 4f occupancy from spectroscopic data. The justification for using a single-impurity Anderson Hamiltonian comes from spectroscopic data like the BIS data discussed here or photoemission and absorption data discussed in other chapters of this book. The fact that A increases, e.g., for Ce-Ni... 

The majority of theoreticians do not take hybridization gaps into account, either because the phenomenon which they want to describe occurs only at the lowest temperatures or because they are not convinced of the existence of the hybridization gap in heavy fermions. However, Czycholl and Schweitzer (1992) in a recent paper take a hybridization gap into account and can thus derive the existing phenomena in a quantitative way. As a general statement we believe that in the year 1992 a breakthrough in the application of the general periodic Anderson Hamiltonian to a hybridization gap has occurred. 

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