Analytical Calculation of the Energy Deposition Spectrum and Average Dose to A Spherical Target By Ion Tracks at All Impact Parameters

Microdosimetry is used to estimate quality factors for risk assessment in radiation protection [1] and to quantify relative biological effectiveness (RBE) for treatment planning of hadron radiation therapy [2]. Radiation physics has shown that energetic ions deposit energy in a complex manner: the track structure. The Local Effect Model (LEM) [3] is often used as an approximation to describe this complex track structure. We have previously calculated an analytical expression for the dose to a spherical target fully located in the penumbra of an ion track using the LEM [4]. In this work, the calculation has been extended to all impact parameters. Furthermore, using these analytical expressions, it was possible to obtain the theoretical energy deposition spectra to a sphere irradiated uniformly.