Energy deposition around swift proton tracks in polymethylmethacrylate: How much and how far

The use of proton beams in several modern technologies to probe or modify the properties of materials, such as proton beam lithography or ion beam cancer therapy, requires us to accurately know the extent to which the energy lost by the swift projectiles in the medium is redistributed radially around their tracks, since this determines several endpoints, such as the resolution of imaging or manufacturing techniques, or even the biological outcomes of radiotherapy. In this paper, the radial distribution of the energy deposited around swift-proton tracks in polymethylmethacrylate (PMMA) by the transport of secondary electrons is obtained by means of a detailed Monte Carlo simulation. The initial energy and angular distributions of the secondary electrons generated by proton impact, as well as the electronic cross sections for the ejection of these electrons, are reliably calculated in the framework of the dielectric formalism, where a realistic electronic excitation spectrum of PMMA is accounted for. The cascade of all secondary electrons generated in PMMA is simulated taking into account the main interactions that occur between these electrons and the condensed phase target. After analyzing the influence that several angular distributions of the electrons generated by the proton beam have on the resulting radial profiles of deposited energy, we conclude that the widely used Rudd and Kim formula should be replaced by the simpler isotropic angular distribution, which leads to radial energy distributions comparable to the ones obtained from more realistic angular distributions. By studying the dependence of the radial dose on the proton energy we recommend lower proton energies than previously published for reducing proximity effects around a proton track. The obtained results are of relevance for assessing the resolution limits of proton beam based imaging and manufacturing techniques.