Radial dose distributions from carbon ions of therapeutic energies calculated with Geant4-DNA

We report on radial dose distributions [Formula: see text] for carbon ions calculated with Geant4-DNA code. These distributions characterize ion tracks on a nanoscale and are important for understanding the biological effects of ion beams. We present data for carbon ion beams in the energy range from 20 to 400 MeV u^-1. To approximate the Monte Carlo results, we developed a simple formula that combines the well-known inverse square distance dependence with a factor correcting [Formula: see text] for small [Formula: see text]. The proposed formula can be used to calculate [Formula: see text] for any energy within the above range and for distances [Formula: see text] from 1 nm to 2 μm with a maximum error not exceeding 14%. This range of distances corresponds to a dose range of over seven orders of magnitude. Differences between our results and those of previously published analytical models are discussed.