Computation of doses for large-angle Coulomb scattering of proton pencil beams

In this work we present a study of the impact of considering higher order terms in Molière's multiple Coulomb scattering (MCS) theory for the purpose of calculating scanning proton pencil beam lateral dose profiles in water. The proton beam profile in air, just before entering the target medium, was modeled with a sum of Gaussians fitted with measured data. The subsequent proton scattering in water was described using the three-term Molière distribution, which covers both small- and large-angle scatterings. We compared measured and computed lateral dose profiles at the 2 cm and at the near-Bragg peak depths for proton pencil beams with energies of 72.5 MeV, 121.2 MeV, 163.9 MeV and 221.8 MeV. At shallow depths, the Coulomb interaction model provided a good description of the profiles for all energies, except for 221.8 MeV. At the near-Bragg peak depths, the Coulomb interaction model provided a good description of the profiles only for the 72.5 MeV. The observed discrepancies may be attributed to the additional contributions from nuclear interactions, which may be quantified only after an accurate description of the MCS. The analysis presented in this work did not require user-adjustable parameters and may be carried out in a similar way for any other media, depths and proton energies.