Effective-charge theory and the electronic stopping power of solids

Electronic stopping powers S of solids for penetrating ions are analyzed on the basis of effective-charge theory, and comprehensive comparisons are made to available data for random stopping. The effective projectile-ion charges Z₁*e, extracted from the data agree to within experimental uncertainties with those calculated in a statistical model, for projectile atomic number ranging from Z₁=1 to Z₁=92 and for projectile velocity v₁v₀≡e². The rise of Z₁* with v₁ fully accounts for an often-quoted apparent deviation of heavy-ion stopping power from the behavior expected in the limit v₁→0. The Bloch and the Z₁³ corrections to the usual formula for S are calculated and found to make no appreciable contribution to presently available data, save possibly to one bromine datum. When v₀v₁3v₀ the analysis requires, and provides, an empirical velocity-dependent proton effective charge Zₚ*e. A theoretical account of Zₚ* is given in terms of velocity and energy criteria for electron stripping. Thomas-Fermi densities for heavy ions are used to calculate Z₁*. Our results lead to an interpolation linear in v₁ for the range 0≤v₁v₀ which gives satisfactory values for S in this low-velocity regime.