Wiklund, K., Olivera, G. H., Brahme, A. and Lind, B. K. Radial Secondary Electron Dose Profiles and Biological Effects in Light-Ion Beams Based on Analytical and Monte Carlo Calculations using Distorted Wave Cross Sections. Radiat. Res. 170, 83–92 (2008).

To speed up dose calculation, an analytical pencil-beam method has been developed to calculate the mean radial dose distributions due to secondary electrons that are set in motion by light ions in water. For comparison, radial dose profiles calculated using a Monte Carlo technique have also been determined. An accurate comparison of the resulting radial dose profiles of the Bragg peak for ¹H , ⁴He² and ⁶Li³ ions has been performed. The double differential cross sections for secondary electron production were calculated using the continuous distorted wave-eikonal initial state method (CDW-EIS). For the secondary electrons that are generated, the radial dose distribution for the analytical case is based on the generalized Gaussian pencil-beam method and the central axis depth-dose distributions are calculated using the Monte Carlo code PENELOPE. In the Monte Carlo case, the PENELOPE code was used to calculate the whole radial dose profile based on CDW data. The present pencil-beam and Monte Carlo calculations agree well at all radii. A radial dose profile that is shallower at small radii and steeper at large radii than the conventional 1/r² is clearly seen with both the Monte Carlo and pencil-beam methods. As expected, since the projectile velocities are the same, the dose profiles of Bragg-peak ions of 0.5 MeV ¹H , 2 MeV ⁴He² and 3 MeV ⁶Li³ are almost the same, with about 30% more δ electrons in the sub keV range from ⁴He² and ⁶Li³ compared to ¹H . A similar behavior is also seen for 1 MeV ¹H , 4 MeV ⁴He² and 6 MeV ⁶Li³ , all classically expected to have the same secondary electron cross sections. The results are promising and indicate a fast and accurate way of calculating the mean radial dose profile.