Effective self energy

When innermost core shells must be treated explicitly, the four-component versions of the GREGP operator can be used, in principle, together with the all-electron relativistic Hamiltonians. The GRECP can describe here some quantum electrodynamics effects (self-energy, vacuum polarization etc.) thus avoiding their direct treatment. One more remark is that the... 

Figure 4. Schematic representation of the coherent potential approximation for a substu-tionally disordered alloy. The vertical strip in (h) denotes the effective self-energy, which is a complex quantity, to be determined by the compatibility requirement between die local and average description.

The remaining S(VP)E contribution has been evaluated in the Uehling approximation by Mallampalli and Sapirstein [60] and Persson et al. [7]. This effective self-energy diagram requires charge renormalization as well as mass renormalization. At present only the contribution of the Uehling term of the effective photon... 

Fig. 17. Effective self energy diagram S(NP)E (left) and effective vacuum polarization diagram NP-VP (right) corresponding to the nuclear polarization. The diagrams marked a (hatched balls) show the polarization insertion into the photon propagator whereas those marked b and c show the actual interaction between electron and nucleus. The shaded lines indicate the nucleus with internal degrees of freedom.

Providing the initial system is large enough, a substitution of the fragment of the electrodes by effective self-energy should introduce no spurious effects, and it makes the system effectively infinite. The conductance can be calculated using the formula ... 

An important question is to what extent can a model retaining nearest-neighbor interactions only be revived by use of effective matrix elements and effective self-energies . Examination of the results in Figure 12 reveals that the effect of the nearest-neighbor and next nearest-neighbor interactions can be approximately accommodated through the expression "... 

If the simulated system uses periodic boundary conditions, the logical long-range interaction includes a lattice sum over all particles with all their images. Apart from some obvious and resolvable corrections for self-energy and for image interaction between excluded pairs, the question has been raised if one really wishes to enhance the effect of the artificial boundary conditions by including lattice sums. The effect of the periodic conditions should at least be evaluated by simulation with different box sizes or by continuum corrections, if applicable (see below). 

Random interface models for ternary systems share the feature with the Widom model and the one-order-parameter Ginzburg-Landau theory (19) that the density of amphiphiles is not allowed to fluctuate independently, but is entirely determined by the distribution of oil and water. However, in contrast to the Ginzburg-Landau approach, they concentrate on the amphiphilic sheets. Self-assembly of amphiphiles into monolayers of given optimal density is premised, and the free energy of the system is reduced to effective free energies of its internal interfaces. In the same spirit, random interface models for binary systems postulate self-assembly into bilayers and intro-... 

Here, an effective one-electron operator matrix has Fock and energy-dependent, self-energy terms. Prom this matrix expression, one may abstract one-electron equations in terms of the generalized Fock and energy-dependent, self-energy operators ... 

In this contribution we will deal with electron-electron correlation in solids and how to learn about these by means of inelastic X-ray scattering both in the regime of small and large momentum transfer. We will compare the predictions of simple models (free electron gas, jellium model) and more sophisticated ones (calculations using the self-energy influenced spectral weight function) to experimental results. In a last step, lattice effects will be included in the theoretical treatment. 

The improvement compared to the representation of Equation (6) is, that self-energy effects are included via the influence of the self-energy T, on A ... 

The solid points show the experimental result, the long dashed line the calculation of a g(< )-modified Lindhard response function according to Equation (6), using g(q) after Utsumi and Ichimaru [5]. The solid line gives the result of a calculation that also takes into account self-energy effects on-shell, that is, introducing the lifetime of the involved states into the calculation according to Equation (14). One can clearly see that the latter reproduces the experimental result quite nicely. 

To make this point clear, one has to look at the involved effects using diagram techniques. Self-energy effects, that is the deformation of the electron cloud around a single electron which then reacts back on this electron, can be divided into two... 

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

Invoking the Hartree-Fock approximation (HFA) (Salem 1966), means that we can replace Una-a in (4.33) by an averaged self-energy U na-a), whereby an effective adatom level of spin a is defined by2... 

A better method is the average t-matrix approximation (ATA) (Korringa 1958), in which the alloy is characterized by an effective medium, which is determined by a non-Hermitean (or effective ) Hamiltonian with complex-energy eigenvalues. The corresponding self-energy is calculated (non-self-... 

A description of nuclear matter as an ideal mixture of protons and neutrons, possibly in (5 equilibrium with electrons and neutrinos, is not sufficient to give a realistic description of dense matter. The account of the interaction between the nucleons can be performed in different ways. For instance we have effective nucleon-nucleon interactions, which reproduce empirical two-nucleon data, e.g. the PARIS and the BONN potential. On the other hand we have effective interactions like the Skyrme interaction, which are able to reproduce nuclear data within the mean-field approximation. The most advanced description is given by the Walecka model, which is based on a relativistic Lagrangian and models the nucleon-nucleon interactions by coupling to effective meson fields. Within the relativistic mean-field approximation, quasi-particles are introduced, which can be parameterized by a self-energy shift and an effective mass. 

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