Review of theories on ionization in fast ion-atom collisions with prospects for applications to hadron therapy

Abstract

This study emphasizes the need for a systematic and in-depth connection between the progress in quantum theory of energetic ion collisions and applications to hadron therapy. Scattering theory for fast ion beams has reached its stage of development where accurate and robustly applicable methodologies can advantageously be exported to applied fields such as space research, fusion energy program, medicine, etc. In particular, distorted wave collision theories at high energies readily provide total, partial and fully differential cross sections for inelastic collisions of ionic projectiles with any target system. By numerous and thorough testings, such theoretical cross sections were found to exhibit excellent agreement with experimental data on atomic targets. Adequate extensions of these methods to molecular targets were also accomplished with computational efforts that are approximately comparable to that for multi-electron atomic targets. This was done by using the standard Slater-type atomic basis functions for any molecular targets, including tissue-equivalent materials (e.g. water) of relevance to hadron therapy. This expertize needs to be brought to medicine through ion transport physics, which most frequently employs the crude Bragg sum rule for obtaining molecular cross sections as linear combination of atomic cross sections. Relativistic distorted wave theories are also available, but not currently in use for modeling the passage of relativistic ions through tissue, as needed in hadron therapy of deep-seated tumors. It is high time for extensive and thorough applications of the well-established distorted wave scattering theories to fast collisions of bare and partially clothed multiple charged ions with water molecule. This type of application would provide the most accurate data bases for various cross sections (on electron capture, excitation, ionization, etc) that can be used as reliable entry data for subsequent Monte Carlo simulations of energy losses of ions during their passage through tissue. In order to gain in overall efficiency, these theoretical cross sections could be precomputed at sufficiently dense multi-variable grids, thus yielding modules for advantageous direct sampling during stochastic simulations. Such a comprehensive strategy could provide both accurate and efficient algorithms that would incorporate the state-of-the-art methodologies from high-energy atomic scattering theory involving ion beams. This is currently missing in the physics part of hadron therapy, since all the major Monte Carlo codes customarily employ atomic cross section data bases that rely almost exclusively upon the Bethe–Bloch formula and some phenomenological expressions with fitting parameters adjusted to the limited sets of experimental data. Crucially, the need is emphasized for the introduction of a still missing Monte Carlo code which could simulate transport of ions together with secondary electrons in tissue. The current main Monte Carlo codes simulate transport of either ions or electrons, but not both simultaneously. However, energetic ions produce a large number of electrons by densely ionizing the traversed tissue and many of them are δ-electrons i.e. capable on their own of ionizing various targets. Due to their light mass and considerable energy, δ-electrons undergo multiple scatterings. Because of this cumulative effect, among all the double strand breaks of DNA molecules of tissue treated by ion therapy, some 70% are produced by δ-electrons. Hence the necessity to simulate transport of δ-electrons produced by primary ion beams. Such types of computations are presently missing from the major ion transport codes. Overall, this work thoroughly analyzes conceptual and computational advances of the leading quantum-mechanical distorted wave theories for energetic ion collisions aimed at applications to medicine. Additionally, the main strategic directions are also indicated to further cross-disciplinary fertilization between medicine and basic research on collision theory of fast heavy ions of relevance to hadron therapy.