Static particle-hole 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... 

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) ... 

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... 

This equation yields a closed expression for the static self energy. The physical significance is to account for interactions and exchange phenomena between the two test particles (or holes) and the (static) particle density of isolated N-particle system. Also the additional (unphysical) components of the extended states take some effect here as well. The discussion of the static self energy and its physical significance will be the main objective of the rest of this paper. 

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