Bragg's Rule of Stopping Power Additivity: A Compilation and Summary of Results

Abstract

Stopping power additivity, as expressed by Bragg's rule, is an important concept in many practical situations involving charged particles. Its validity has been investigated in a large number of studies and the wide range of data is confusing and at times conflicting. No previous comprehensive survey of the data has been undertaken. Thus a compilation is attempted here of a hundred or so papers which have included tests of Bragg's rule. Their main results are indicated and a summary is given of the effects of chemical binding and phase on the stopping power of heavy charged particles. Such effects are confirmed on the evidence available. Chemical binding effects become more significant for materials containing low-Z constituents and as energy falls into and through the transition region. Deviations of up to 50% have been observed in atomic stopping cross sections extracted from measurements on hydrocarbons. There is still some conflicting evidence appearing on phase effects. However, in general a broad consensus is emerging indicating significant differences in H/sub 2/O and organic and similar materials. Stopping cross sections in the vapor phase are greater by up to approx. 5 or 10% at energies around those of the stopping power maximum for protonsmore » and He ions. The effects decrease as energy increases.« less