Effective charge and related/unrelated quantities in heavy-ion stopping

Abstract

Stopping cross sections for swift heavy ions are commonly parameterized in terms of a velocity-dependent effective charge defined with reference to proton or helium stopping. This assumes projectile screening by core electrons to be a dominating factor governing the velocity dependence of the stopping cross section. In this note we demonstrate, on the basis of improved theoretical estimates of stopping cross sections, that projectile screening only affects the quantitative details of the velocity dependence of the effective charge while the general behavior reflects the transition from the Born to the classical regime. This is consistent with the experience that effective charges derived from measured stopping cross sections show dependencies on projectile and target atomic number which differ distinctly from those of the equilibrium projectile charge. It follows that there is no theoretical basis for the effective-charge concept as it is commonly used in heavy-ion stopping.