Surface Electronic Response in the Random Phase Approximation and Infinite Barrier Model: Surface Plasmons, Electron-Hole Pairs and the Interaction With External Particles

We set up the formalism for obtaining the self-consistent fully screened Coulomb interaction propagator in the region outside the jellium metal. We calculate and discuss the spectral densities of surface electronic excitations for the case of the Infinite and Semiclassical Infinite Barrier Models, in the Random Phase Approximation, and apply them to study the low-energy electron-hole part of the spectrum, as well as dispersion, damping and weight of the surface plasmon poles. We show how this formalism describes the interaction of external particles with the surface electronic excitations, specifically studying the particle-surface van der Waals interactions, energy shifts of a charged particle near a surface and the EELS experiments. We try to compare the given approach with the vast amount of the already existing related work on these problems.