Aggregates of atoms and their stopping cross sections

The problem of deriving universal atomic stopping cross sections from measurements performed in real physical targets is discussed with regard to the influence of the bonds on the stopping cross sections, which exists whenever atoms join to form molecules or a solid. This influence has to be considered for all investigated substances, except for the noble gases. The influence of the bonds on the stopping cross sections, which may lead to an observable deviation from Bragg's rule, can be quite large. In addition to the direct influence of the bonds, aggregates of atoms in the form of liquids or solids have a stopping cross section which differs from that of the same substance in the gaseous state, the so-called physical state effect. We show that a separate determination of these influences is not possible from experimental results alone, which means that it is not possible in general to extract stopping cross sections referring to free atoms from values measured in real physical targets.