The water equivalence of solid materials used for dosimetry with small proton beams

Various solid materials are used instead of water for absolute dosimetry with small proton beams. This may result in a dose measurement different to that in water, even when the range of protons in the phantom material is considered correctly. This dose difference is caused by the diverse cross sections for inelastic nuclear scattering in water and in the phantom materials respectively. To estimate the magnitude of this effect, flux and dose measurements with a 177 MeV proton pencil beam having a width of 0.6 cm (FWHM) were performed. The proton flux and the deposited dose in the beam path were determined behind water, lucite, polyethylene, teflon, and aluminum of diverse thicknesses. The number of out-scattered protons due to inelastic nuclear scattering was determined for water and the different materials. The ratios of the number of scattered protons in the materials relative to that in water were found to be 1.20 for lucite, 1.16 for polyethylene, 1.22 for teflon, and 1.03 for aluminum. The difference between the deposited dose in water and in the phantom materials taken in the center of the proton pencil beam, was estimated from the flux measurements, always taking the different ranges of protons in the materials into account. The estimated dose difference relative to water in 15 cm water equivalent thickness was -2.3% for lucite, -1.7% for polyethylene, -2.5% for teflon, and -0.4% for aluminum. The dose deviation was verified by a measurement using an ionization chamber. It should be noted that the dose error is larger when the effective point of measurement in the material is deeper or when the energy is higher.