Energy loss of a charged particle moving outside a nano-dielectric sphere covered with infinitesimally thin metal film

In this paper, we investigate the electronic excitations induced by a charged particle moving outside a nano-dielectric sphere covered with infinitesimally thin metal film by using the linearized quantum hydrodynamic (QHD) theory. General expressions of the induced potential of the electron and the stopping power of the charged particle are derived in spherical coordinates systems. In our calculations, the spherical distribution of the induced potential for different particle speed is examined. The results indicate that an oscillatory wake effect exists in the electron gas during the interactions. In addition, the dependence of the stopping power on a charged particle position and relative permittivity of a dielectric sphere is analyzed.