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. 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.