  Dose calculation for radiotherapy with protons and heavier ions deals with a
large volume of path integrals involving a scattering power of body tissue.
This work provides a simple model for such demanding applications. There is an
approximate linearity between RMS end-point displacement and range of incident
particles in water, empirically found in measurements and detailed
calculations. This fact was translated into a simple linear formula, from which
the scattering power that is only inversely proportional to residual range was
derived. The simplicity enabled analytical formulation for ions stopping in
water, which was designed to be equivalent with the extended Highland model and
agreed with measurements within 2% or 0.02 cm in RMS displacement. The
simplicity will also improve the efficiency of numerical path integrals in the
presence of heterogeneity.
