Creating a spread-out Bragg peak in proton beams

The model of Bortfeld and Schlegel (1996 Phys. Med. Biol. 41 1331-9) for determining the weights of proton beams required to create a spread-out Bragg peak (SOBP) gives a significantly tilted SOBP. However, by arbitrarily varying its parameter p, which relates the range of protons to their energy, we have been able to create satisfactory SOBPs. MCNPX Monte Carlo calculations have been carried out to determine p, demonstrating the success of this modification. Optimal values of p are tabulated for various combinations of maximum beam energy E(0) (50, 100, 150, 200 and 250 MeV) and SOBP width χ (15%, 20%, 25%, 30%, 35% and 40%), as well as for a correction factor needed to calculate the SOBP dose. An example shows the application of these results to analyzing the dose deposited by deuterons and alpha particles in broad proton beams.