The atomic number of a material exhibits a strong and fundamental relationship with the nature of radiation interactions within that medium. There are numerous mathematical descriptions of different interaction processes that are dependent on the atomic number, Z. When dealing with composite media (i.e. a bulk material composed of more than one element), one therefore encounters the difficulty of defining Z. An effective atomic number in this context is equivalent to the atomic number but is used for
compounds (e.g. water) and mixtures of different materials (such as tissue and bone). This is of most interest in terms of radiation interaction with composite materials. For bulk interaction properties, it can be useful to define an effective atomic number for a composite medium and, depending on the context, this may be done in different ways. Such methods include (i) a simple mass-weighted average, (ii) a power-law type method with some (very approximate) relationship to radiation interaction properties or (iii) methods involving calculation based on interaction cross sections. The latter is the most accurate approach (Taylor 2012), and the other more simplified approaches are often inaccurate even when used in a relative fashion for comparing materials.
In many textbooks and scientific publications, the following - simplistic and often dubious - sort of method is employed. One such proposed formula for the effective atomic number, ''Z''
eff, is as follows: