Many-body theory of effective local potentials for electronic excitations. II. General theory

The major purpose of the present paper is to find effective energy-dependent one-electron potentials for core excitations in atoms and solids in terms of the frequency-dependent density response of the system. In the case of the photoionization amplitude we demonstrate how all effects of many-electron interactions within the random phase approximation with exchange (RPAE) can be represented by an effective one-electron wave function or an effective, nonlocal, electron-photon interaction. We also demonstrate the usefulness of intermediate schemes with one-electron basis states of the Hartree-Fock average-of-configuration potentials (V^N-1) or the local-density approximation (LDA) with which one calculates the density response within the RPA (no ``exchange''), and we make some comparisons with the time-dependent LDA. We also demonstrate how the form of an effective one-electron wave function depends on the choice of dipole-length or dipole-velocity operator. We finally express the RPAE photoionization amplitude in terms of an average amplitude with a Hartree-Fock ¹P wave function and an average dipole-length--dipole-velocity operator and a correction with a correlation wave function and a difference dipole-length--dipole-velocity operator.