Effective charges of ions and the stopping power of dense media

Projectiles of atomic number Z1 moving at velocity ν1 in dense media with ionic charge Q1 (ν1) by general arguments lose energy at a rate as if they were in an effective charge state Z1∗ > Q1. We derive Z1∗/Q1 in a dielectric-response approximation and test the predictions on new low-velocity precision experiments and high-velocity channeling experiments. The “Z2 oscillations” of stopping powers in targets of atomic number Z2 are shown to be related to the variations of the conduction-electron densities in the periodic system. In a different vein, the electronic stopping power of stars for massive neutrinos, through the interaction with the neutrino magnetic moment, is calculated, and some cosmological inferences are drawn.