Hole self-energy

Fig. 9a-g. The core hole self-energy 2j(E). (a) Expansion of the single-hole j... 

Core-Hole Self-Energy (E) Formal Theory and Approximative Treatment... 

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

B The dynamic particle-hole self energy C The zeroth-order degenerate states D First order self energy... 

A Formal definition of the Hilbert space Y B Static particle-particle self energy for electrons C Static particle-hole self energy for electrons... 

The first order of the particle-hole self energy is readily obtained from the expression (68) by replacing the reference states and i ) by their zeroth orders ) and respectively, and by considering the interaction part... 

In a recent publication we have investigated this first order approximation to the particle-hole self energy for the choice y>) = o ) for the reference state tp) and starting from a Hartree-Fock zeroth order [21]. This particular approximation to the particle-hole self energy is referred to as First Order Static Excitation Potential (FOSEP). In terms of the matrix elements of the Hamiltonian the FOSEP approximation of the primary block H reads... 

APPENDIX C STATIC PARTICLE-HOLE SELF ENERGY FOR... 

In this appendix we present the interaction part (at,a, y o, a,<) of the static particle-hole self energy discussed in Sec. VIC. We assume Coulomb interacting electrons with the usual position space representation (106) of the two-body interaction V. The expression for the interaction part of the static self particle-hole self energy can then be readily evaluated, either from the definitions of the extended states (1) or from Eq. (68) ... 

FIGURE 5.5. Virtual excitations contributing to the electron and hole self-energies [2 + )(e) and 2 + >(h), respectively] in the (N + 1)-particle state. 

TABLE 5.4. Different Physical Quantities Contributing to the Formation of the Quasi-Particle Energy-Band Gap in the Alternating trans PA One-Particle Energies e(HF), Electron and Hole Self-Energies, 2(e) and 2(h), Respectively, and Quasi-Particle Energies e(QP)<2 > ... 

For an energy band state, this is given by the sum of corresponding HF energy and the electronic and hole self energies of the corresponding state which means the correlation-corrected band state. 

One can interpret the correction terms appearing in addition to the HF band energies in these equations as electron and hole self-energies [5 (e) and D(h), respectively). For this purpose one can introduce the notation... 

Before explicitly calculating these quantities, some of their qualitative trends can be observed. For the bottom of the conduction band the denominators of rj in equation (59) are always negative (see Figure 1), therefore the electron selfenergy shifts this state downward. Also, since the values of rff in equation (60) are negative, the hole self-energy produces a positive (upward) shift. (We note that in the... 

Figure 1 Virtual excitations contributing to the electron and hole self-energies particle state...

The structures of Eq. (2.20) would be similar to that of Eq. (2.33) if n°((A)) in Eq. (2.20) is retained. This is approximately Frue in most cases. The major difference would be that would be replaced by in Eqs. (2.33). Since uJpj differs from IaJ ° by the renormalization effects coming from the particle or hole self-energies, an investigation of the selfenergies would yield these effects. Also, it is clear from the structure of Eqs. (2.33) and (2.34) that K(c0) contains the... 

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