Electron-Ion Interactions and Many-Body Effects in Simple Metals

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Abstract
In this paper we derive expressions for a number of properties of simple metals, using a spatially local energy-independent pseudopotential to represent the electron-ion interaction. Quantities are expressed in terms of correlation functions for the homogeneous electron gas and matrix elements of the electron-ion pseudopotential; electron-electron interactions are included to all orders in perturbation theory, and electron-ion interactions to low order. First, we consider the long-wavelength finite-frequency dielectric function and generalize some results of Hopfield; the dielectric function is then used to derive expressions for optical properties, and the frequency and damping of long-wavelength plasma oscillations. Second, we consider the phonon spectrum; expressions for the phonon dynamical matrix are derived, taking into account the influence of the periodic ionic lattice on the motion of electrons. It is shown that to obtain results consistent with expressions for the elastic constants derived from expressions for the energy of the system calculated to the second order in the electron-ion interaction, one must include in the calculation of the phonon dynamical matrix some terms of third and fourth order in the electron-ion interaction. A detailed discussion of the long-wavelength behavior of the dynamical matrix is given.