Influence of the delta ray production threshold on water-to-air stopping power ratio calculations for carbon ion beam radiotherapy

Previous calculations of the water-to-air stopping power ratio (sw,air) for carbon ion beams did not involve tracking of delta ray electrons, even though previous calculations with protons predict an effect up to 1%. We investigate the effect of the delta ray production threshold insw,air calculations and propose an empirical expression which takes into account the effect of the delta ray threshold as well as the uncertainty in the mean ionization potentials (I-values) of air and water. The formula is derived from the results of Monte Carlo calculations using the most up-to-date experimental data for I-values and a delta ray production threshold of 10 keV. It allows us to reduce the standard uncertainty insw,air below 0.8%, instead of the current 2% given in international protocols, which results in a reduction of the overall uncertainty for absolute dosimetry based on air-filled ionization chambers. (Some figures may appear in colour only in the online journal)