Total Reaction Cross Section in Nucleus-nucleus Reactions

The transportation of heavy ions in matter is a subject of much interest in several fields of science. An important input for simulations of this process is the total reaction cross section, which is defined as the total ( $\sigma_{T}$) minus the elastic ( $\sigma_{el}$) cross section for nucleus-nucleus reactions:

$$\sigma_{R} = \sigma_{T} - \sigma_{el} .$$

The total reaction cross section has been studied both theoretically and experimentally and several empirical parameterizations of it have been developed. In Geant4 the total reaction cross sections are calculated using four such parameterizations: the Sihver[#!nnc.Sihver93!#], Kox[#!nnc.Kox87!#], Shen[#!nnc.Shen89!#] and Tripathi[#!nnc.Tripathi97!#] formulae. Each of these is discussed in order below.