Lateral spread of dose distribution by therapeutic proton beams in liquid water

We have calculated the lateral spread of the dose distribution of protons in liquid water by means of the SEICS (Simulation of Energetic Ions and Clusters through Solids) code, which properly accounts for the electronic stopping force (including energy-loss straggling), multiple elastic scattering with the target nuclei, dynamical electron charge-exchange processes and nuclear fragmentation reactions between the projectile and the nuclei of the target. Due to the multiple elastic scattering processes part of the proton energy may be deposited at a given lateral distance from the initial beam direction, which is quantified by the root mean square radius (rrms). We find in our simulations that the rrms follows a parabolic dependence as a function of the depth in the target and the quotient between the rrms at the Bragg peak and the depth of the Bragg peak is around 3% independently of the proton energy. A rather good agreement is obtained when comparing our results of rrms with experimental data and with other models.