Self-energy diagrams

From considerations on translational symmetry in the limit of a stereoregular polymer, which are more conveniently analyzed in terms of conservation constraints on momenta at interaction vertices and within self-energy diagrams (31), each Ih line can be easily shown (see e.g. Figure 4 for a second-order process)... 

After this necessary excursion into the broad field of electron-electron interactions as described in diagrammatic language and by certain approximations, the effects of electron correlations beyond the RRPA approach can be summarized by using the following rules (neglecting the photoelectron s self-energy diagram) ISCI and FISCI must be taken explicitly into account, and the theoretical ionization threshold has to be adapted to the experimental value. 

Only the direct self-energy diagrams (e.g. Fig. 9 e) can be interpreted in terms of classical physics. The exchange processes are sometimes important and must be included in actual calculations. However, they do not change the basic physical picture, and in this qualitative discussion we therefore only consider the direct processes. 

Fig. lla-e. Monopole relaxation in response to a localized core hole (a) general self-energy diagram (b) monopole part of (a) (c) real space picture of monopole relaxation, illustrating the radial contraction of a relaxing shell typical core level spectra in (d) atoms and molecules and (e) metals... 

We can now define the connection between the physical relaxation processes and the internal structure of the direct self-energy diagram in Fig. 11a ... 

Fig. 12a-e. Non-monopole (quadrupole) relaxation and shape distortion of a core hole in open shell type of situations (a) Lowest order self-energy diagram (b) one-electron picture of the pulling down of empty levels below the Fermi level (c) shape distortion of one-electron orbitals due to quadrupole relaxation (d, e) schematic core level spectra in the case of (d) closed and (e) open ground state shell structure (d)... 

We shall now break down the renormalized self-energy diagram in Fig. 19 c in terms of effective two-body interactions suitable for explicit calculations. In analogy with the Dyson equation in Fig. 19 a, the total three-body, i.e. one-particle-two-hole (phh),... 

Fig. 24a-i. One-electron level pictures and self-energy diagrams for dynamic relaxation of 4 s and 4p holes, (a)—(c) and (f, g) describe giant Coster-Kronig fluctuation (full plus dashed arrows) and decay processes (full arrows) while (d, e) and (f,) (h, i) correspondingly describe Coster-Kronig fluctuations and decay processes... 

Fig. 28a-h. 4 p self-energy diagrams in a case where a 4d24f ionic excited level dominates the excitation spectrum (see text and compare with Figs. 10, 17-19)... 

Fig. 38a-f. One-electron level °u pictures and self-energy diagrams for fluctuation and relaxa- °g tion of hole levels within a molecular model-level structure oj, (for explanation of (a) to (f) see text)... 

Fig. 40a-g. Self-energy diagrams describing relaxation and correlation in the valence region of the model level structure in Fig. 39 (for further explanations see text)... 

Fig. 56 a-f. Self-energy diagrams describing the most important satellite excitations in the valence region of QH, (for further explanations, see text also cf. Fig. 40)... 

Fig. 63 a-i. Core hole self-energy diagrams describing relaxations in a transition-metal compound (see text)... 

To illustrate how this works, we consider a simple example of the one-loop self-energy diagram on the mass shell p2 = m2, shown in Fig.l. 

X at the point xq, and the skeletons of the screened self-energy diagrams with a self-energy on the left and on the right are defined as ... 

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.

Cederbaum and co-workersdo not explicitly evaluate diagrams that include effects of the 5-block of basis operators in their diagrammatic Green s function approach. Cederbaum has, however, employed a self-consistent procedure that iteratively replaces unperturbed Green s function, Gq, lines with perturbed ones, G, in self-energy diagrams. This results... 

Wendin also implicitly includes part of the effect of the 5- and higher blocks by replacing hole orbital energies in the denominators of self-energy diagrams with ASCF values for the ionization potentials for the removal of an electron from the orbitals in question. Orbital relaxation is treated in this fashion. This approach is likely to be reasonable for holes in core levels, the situation with which Wendin is concerned, since relaxation effects tend to be greater than changes in correlation for ionization from these levels. 

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