Proton stopping powers averaged over beam energy spectra

Abstract

Stopping powers averaged over the proton energy spectra at various depths inwater and a tissue-like material were calculated for proton beams with initialenergies between 50 and 250 MeV. The analysis was made for proton beams with aspread-out Bragg peak (SOBP) to assess in particular the variations of stoppingpower with depth in the SOBP plateau region. Nuclear interactions were accountedfor in determination of the proton energy spectra. In modulated beams, stoppingpower varies considerably with depth along the plateau region of the spread-outpeak. Moreover, stopping powers at the same water depth may differ from eachother by up to 20% if referring to modulated or non-modulated beams.Calculations of water-air mass stopping power ratios were also performed, withand without the inclusion of nuclear interactions, for modulated and non-modulated beams. The stopping power ratios do not depend significantly on protonenergy, and this makes the effect of accounting for nuclear interactions inproton fluence calculation negligible. For the same reason the stopping powerratios for modulated beams do not appreciably differ from those referred to non-modulated beams with the same Emax at the same depth in water. Thepresent results also show that the dependence of stopping power on energy spreadand spatial divergence for proton beams is not negligible in some conditions.Some conclusions are drawn on the possibility of using the residual range as adescriptor of the proton beam quality for different experimental beamconditions.