EFFECTIVE-CHARGE THEORY AND 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 v1 v0 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 v0 v1 3v0 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≤v1 v0 which gives satisfactory values for S in this low-velocity regime. © 1978 The American Physical Society.