Memory effect on energy losses of charged particles moving parallel to solid surface

Theoretical derivations were made for the induced potential and the stopping power of a charged particle moving close and parallel to the surface of a solid. It was illustrated that the induced potential produced by the interaction of particle and solid depended not only on the velocity but also on the previous velocity of the particle before its last inelastic interaction. Another words, the particle kept a memory on its previous velocity, v0, in determining the stopping power for the particle of velocity v. Based on the dielectric response theory, formulas were derived for the induced potential and the stopping power with memory effect. An extended Drude dielectric function with spatial dispersion was used in the application of these formulas for a proton moving parallel to Si surface. It was found that the induced potential with memory effect lay between induced potentials without memory effect for constant velocities v0 and v. The memory effect was manifest as the proton changes its velocity in the previous inelastic interaction. This memory effect also reduced the stopping power of the proton. The formulas derived in the present work can be applied to any solid surface and charged particle moving with arbitrary parallel trajectory either inside or outside the solid.