Stopping power of electron liquid for slow quantum projectiles

We revisit the problem of deceleration of a charge moving in a medium. Going beyond the traditional approach, which relies on Ehrenfest dynamics, we treat the projectile fully quantum mechanically, on the same footing as the electrons of the target. In order to separate the dynamics of the projectile from that of the electrons, we employ the Exact Factorization method. We illustrate the resulting theory by applying it to the problem of the stopping power (SP) of a jellium-model metal for slowly moving charges. The quantum mechanical nature of particles manifests itself remarkably in the differences in the SP for projectiles of the same charge moving with the same velocity, but having different masses.