The Radial Distribution of Dose around the Path of a Heavy Ion in Liquid Water

Monte Carlo calculations of the radial distribution of dose in liquid water, incorporating energy deposition due to primary excitations and ionizations, have been performed for protons of energy 1, 10, 20, 50, and 100 MeV. By combining these results with earlier semi-empirical formulae used in track structure theory calculations, a corrected analytic formulation has been developed which on radial integration closely reproduces the value of stopping power for protons in the energy range 0.1–1000 MeV. After including a β-dependent ‘effective charge’ formula, this corrected formulation is tested against all published measurements of radial distribution of dose from energetic ions in gaseous media. Though some inconsistencies at the closest and the farthest reaches of the radial distribution of dose remain, the overall agreement is very satisfactory, indicating that the ‘effective charge’ Z*, and Z*2/β 2 scaling are phenomenologically valid concepts for describing the radial dose from heavy ions of energies above ~0.5MeV/amu.