Nonlinear interaction of charged particles with a free electron gas beyond the random-phase.pdf

a r X i v : c o n d - m a t / 0 0 0 7 0 5 2 v 1 [ c o n d - m a t .m t r l - s c i ] 4 J u l 2 0 0 0 Nonlinear interaction of charged particles with a free electron gas beyond the random-phase approximation T. del R??o Gaztelurrutia1 and J. M. Pitarke2,3 1 Fisika Aplikatua Saila, Industri eta Telekomunikazio Ingeniarien Goi Eskola Teknikoa, Urkijo Zumarkalea z/g, S-48013 Bilbo, Spain 2 Materia Kondentsatuaren Fisika Saila, Zientzi Fakultatea, Euskal Herriko Unibertsitatea, 644 Posta kutxatila, 48080 Bilbo, Basque Country, Spain 3 Donostia International Physics Center (DIPC) and Centro Mixto CSIC-UPV/EHU, Donostia, Basque Country, Spain (February 6, 2008) A nonlinear description of the interaction of charged particles penetrating a solid has become of basic importance in the interpretation of a variety of physical phenomena. Here we develop a many- body theoretical approach to the quadratic decay rate, energy loss, and wake potential of charged particles moving in an interacting free electron gas. Explicit expressions for these quantities are obtained either within the random-phase approximation (RPA) or with full inclusion of short-range exchange and correlation effects. The Z31 correction to the energy loss of ions is evaluated beyond RPA, in the limit of low velocities. When charged particles pass through a solid, energy can be lost to the medium through various types of elas- tic and inelastic collision processes.1 While at relativis- tic velocities radiative losses may become important, for moving charged particles in the non-relativistic regime the energy loss is primarily due to electron-electron (e-e) interactions giving rise to the generation of electron-hole pairs, collective excitations such as plasmons, and inner- shell excitations and ionizations. Energy losses due to nuclear recoil are negligible, unless the projectile veloc- ity is very small compared to the mean speed of electrons in the solid.2 The inelastic decay rate of charged particles in