QUADRATIC RESPONSE THEORY OF THE ENERGY-LOSS OF CHARGED-PARTICLES IN AN ELECTRON-GAS

A quadratic response theory of the energy loss of charged particles in matter is developed, following a diagrammatic analysis of the many-bo dy interactions between a moving charge and the electron gas. The line ar and quadratic density response functions of the medium are evaluate d in the random-phase approximation (RPA), and a result for the stoppi ng power is obtained, up to third order in the ion charge, Z(1)e, for a wide range of particle velocities. The low- and high-velocity limits of the full RPA result are also studied, and a local plasma approxima tion is used to show that our calculations are in good agreement with measurements of the energy loss of protons and antiprotons in silicon.