## Many-body Theory of a Rapidly Varying Inhomogeneous Electron Gas |

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approximation atom boundary condition calculations considered correlation effects correlation energy density fluctuation density variation diagrams dielectric function dipole e-e interactions eigenfunctions elec electron density EQ(p equation equivalent exact excitation Fermi sea Fermi sphere Fermi surface formalism free electron Friedel oscillations gases Green's function Hamiltonian Hartree-Fock image technique infinite inhomogeneous electron gas interacting electron interaction propagator Kohn Langer and Vosko linear Loucks and Cutler many-body effects many-body theory mathematical matrix momentum space non-interacting electron numerical obtained periodic lattice periodic potential physical plane wave plasma frequency plasma oscillation point of view polarizable polarization charge poles present propagating electron quantitative quasi-particle real metals result scattering screened exchange screening charge density self-energy self-energy processes shown in Figure sine wave single-particle surface barrier surface effects surface impurity screening surface plasmon surface potential surface region term theoretic Thomas-Fermi tions total energy treated vertex function wavefunctions wavelength