Improved parametrization of the transparency parameter in Kox and Shen models of total reaction cross sections

The total reaction cross section is an essential quantity in particle and heavy-ion transport codes when determining the mean free path of a transported particle. Many transport codes determine the distance a particle is transported before it collides with the target or is stopped in the target material, with the Monte Carlo (MC) method using semiempirical parametrization models for the total reaction cross sections. In order to improve the well-known Kox and Shen models of total reaction cross sections and allow the models to be used at energies below 30 MeV/nucleon, we propose a modified parametrization of the transparency parameter. We also report that the Kox and Shen models have a projectile-target asymmetry and should be used so that the lighter nucleus is always treated as the projectile