The Schiff angular bremsstrahlung distribution from composite media

The Schiff differential for the angular distribution of bremsstrahlung is widely employed, but calculations involving composite materials (i.e. compounds and mixtures) are often undertaken in a somewhat ad hoc fashion. In this work, we suggest an alternative approach to power-law estimates of the effective atomic number utilising Seltzer and Berger’s combined approach in order to generate single-valued effective atomic numbers applicable over a large energy range (in the worst case deviation from constancy of about 2% between 10 keV and 1 GeV). Differences with power-law estimates of Z for composites are potentially significant, particularly for low-Z media such as biological or surrogate materials as relevant within the context of medical physics. As an example, soft tissue differs by >70% and cortical bone differs by >85%, while for high-Z composites such as a tungsten–rhenium alloy the difference is of the order of 1%. Use of the normalised Schiff formula for shape only does not exhibit strong Z dependence. Consequently, in such contexts the differences are negligible – the power-law approach overestimates the magnitude by 1.05% in the case of water and underestimates it by <0.1% for the high-Z alloys. The differences in the distribution are most pronounced for small angles and where the bremsstrahlung quanta are low energy.