Stopping Power of Electron Liquid for Slow Quantum Projectiles

We revisit the problem of the deceleration of a charge moving in a medium. In the low-velocity limit of the projectile, we construct the fully nonlinear (in the charge–target interaction) theory of the stopping power (SP), which goes beyond the classical Ehrenfest dynamics. In order to separate the motion of the projectile from that of the electrons of the target, we employ the Exact Factorization method. We illustrate the resulting theory by applying it to the problem of SP of a jellium-model metal for slowly moving charges. The quantum mechanical nature of the projectile manifests itself in the differences in the SP for projectiles of the same charge moving with the same velocity but having different masses.