Departures from Bragg's rule of stopping power additivity for ions in dosimetric and related materials

Abstract

A survey of tests of Bragg's rule of stopping power additivity is updated, reviewing recent evidence on chemical binding and physical state effects on ion stopping power in dosimetric and related materials. A general failure of simple additivity of constituent element stopping powers is well established, depending on the atomic numbers of the compound components and the type of bonding involved. Magnitudes of discrepancies are subject to some uncertainty, but this is reducing. A modified additivity based on separation and summing of core and bond contributions can be used to fit experimental data reasonably well. Phase effects in low- Z dosimetric materials are ∼10%, near the stopping power maximum for light ions, decreasing as energy increases. ϵ(vapour)> ϵ(condensed phase). Lower energy trends still contain some uncertainties. The accuracy of stopping power measurements is often insufficient to detect and quantify the effects of interest unambiguously. In the absence of adequate measurements or theory for some materials of interest over the wide energy range of interest, some practical empirical guidelines are suggested to provide approximate corrections to simple additivity values for proton stopping power.