  In proton therapy both the energy, which determines the range, and the distal
slope, which reflects the rate at which the protons decelerate, are of import
if we are to ensure accurate dose deposition and maximum tissue sparing. This
publication describes a Geant4 model and presents a two-dimensional polynomial
relationship between energy, the energy spread and the distal slope for beams
with Gaussian energy spectra for proton therapy. This simple polynomial
relationship will be useful for non-invasive or minimally invasive near
real-time monitoring of the energy and energy spread of a proton therapy beam.
