SELF-ENERGY OF A CHARGED-PARTICLE PLACED IN A GAP BETWEEN 2 METAL-SURFACES AND NEAR A METALLIC SLAB

We derive general expressions for the self-energy of a charged particl e placed in the gap between two metal surfaces and near a metallic sla b. Treating the electron gas in the metal within the hydrodynamic appr oximation, the self-energy of a charged particle is obtained, taking i nto account the dispersion of the surface plasmons and the effect of t he recoil of the charged particle. We show that the self-energy satura tes rates to a finite negative value at the metal surface and inclusio n of recoil and dispersion reduces the magnitude of the self-energy.