A combined molecular dynamics and Monte Carlo simulation of the spatial distribution of energy deposition by proton beams in liquid water.

We have evaluated the spatial distribution of energy deposition by proton beams in liquid water using the simulation code SEICS (Simulation of Energetic Ions and Clusters through Solids), which combines molecular dynamics and Monte Carlo techniques and includes the main interaction phenomena between the projectile and the target constituents: (i) the electronic stopping force due to energy loss to target electronic excitations, including fluctuations due to the energy-loss straggling, (ii) the elastic scattering with the target nuclei, with their corresponding energy loss and (iii) the dynamical changes in projectile charge state due to electronic capture and loss processes. An important feature of SEICS is the accurate account of the excitation spectrum of liquid water, based on a consistent solid-state description of its energy-loss-function over the whole energy and momentum space. We analyse how the above-mentioned interactions affect the depth distribution of the energy delivered in liquid water by proton beams with incident energies of the order of several MeV. Our simulations show that the position of the Bragg peak is determined mainly by the stopping power, whereas its width can be attributed to the energy-loss straggling. Multiple elastic scattering processes contribute slightly only at the distal part of the Bragg peak. The charge state of the projectiles only changes when approaching the end of their trajectories, i.e. near the Bragg peak. We have also simulated the proton-beam energy distribution at several depths in the liquid water target, and found that it is determined mainly by the fluctuation in the energy loss of the projectile, evaluated through the energy-loss straggling. We conclude that a proper description of the target excitation spectrum as well as the inclusion of the energy-loss straggling is essential in the calculation of the proton beam depth-dose distribution.