  Purpose: Beam range control is the essence of radiotherapy with heavy charged
particles. In conventional broad-beam delivery, fine range adjustment is
achieved by insertion of range shifting and compensating materials. In
dosimetry, solid phantoms are often used for convenience. These materials
should ideally be equivalent to water. In this study, we evaluated dosimetric
water equivalence of four common plastics, HDPE, PMMA, PET, and POM.
  Methods: Using the Bethe formula for energy loss, the Gottschalk formula for
multiple scattering, and the Sihver formula for nuclear interactions, we
calculated the effective densities of the plastics for these interactions. We
experimentally measured variation of the Bragg peak of carbon-ion beams by
insertion of HDPE, PMMA, and POM, which were compared with analytical model
calculations.
  Results: The theoretical calculation resulted in slightly reduced multiple
scattering and severely increased nuclear interactions for HDPE, compared to
water and the other plastics. The increase in attenuation of carbon ions for
20-cm range shift was experimentally measured to be 8.9\% for HDPE, 2.5\% for
PMMA, and 0.0\% for POM while PET was theoretically estimated to be in between
PMMA and POM. The agreement between the measurements and the calculations was
about 1\% or better.
  Conclusions: For carbon-ion beams, POM was dosimetrically indistinguishable
from water and the best of the plastics examined in this study. The poorest was
HDPE, which would reduce the Bragg peak by 0.45\% per 1-cm range shift,
although with marginal superiority for reduced multiple scattering. Between the
two clear plastics, PET would be superior to PMMA in dosimetric water
equivalence.
