Z1 oscillations and charge state in electronic stopping power from first principles

Abstract

The energy transfer rate from a projectile nucleus to the electrons of the matter it traverses depends on the charge of that projectile, Q= e Z1. At low projectile velocities the friction coefficient is known to oscillate with atomic number Z1, since core electrons travel with the projectile screening its charge. The effective charge increases with velocity and oscillations disappear. That effect is studied here calculating electronic stopping power from first principles for O and Mg projectiles shooting through bulk Al, using real-time time-dependent density-functional theory. Both projectiles represent maximum and minimum of the first Z1 oscillation, respectively. The oscillation is found to be very sensitive to the direction of propagation, in spite of Al being quite an ideal metal for many purposes. The critical velocity for the oscillation disappearance ranges between below 0.1 a.u. and beyond 1 a.u. for the explored trajectories. The charge state is independently quantified with Hirshfeld and Voronoi analyses, offering remarkably consistent results in spite of their very different partition methods, as well as with an effective definition based on the stopping power itself. They display a gradual undressing of the projectile's core electrons with increasing velocity in qualitative accordance with expectations. However, electron density plots in real space present a richer picture in which the undressing is partly due to the electrons trailing behind the projectile, suggesting possible phenomenological descriptions correcting for the deformation of the density in terms of multipoles beyond the net charge. The plots also offer insights into dissipation by core electrons.