Image forces for a point-like dipole near a plane metal surface: An account of the spatial dispersion of dielectric permittivity

Image-force energy profiles were calculated for a constant point-like dipole located in a dispersionless semi-infinite medium adjacent to a medium with the spatial dispersion of its dielectric permittivity. Three models for the substrate were considered: classical (dispersionless), Thomas–Fermi (classical, but taking non-local screening effects into account), and Schulze–Unger (the approximation to the quantum–mechanical non-local Lindhard dependence, reproducing short-range spatial asymptotics correctly). The results obtained taking into account the non-local character of charge-carrier screening differ drastically from those obtained in the classical limit. Hence, classical electrostatics is inadequate, when being applied to analyze the dipole energy at the interface between two polarizable media. In particular, non-local screening results in finite values of the dipole image force energies at the interfaces.