Range spectra in electron penetration problems.

The theory of electron penetration as predicted by the Fokker-Planck equation is first reviewed within a restricted context that considers the multiple scattering and transport of charged particles. We then broaden the context and show that range straggling effects also fit successfully into this framework, which completes an electron model initiated by Yang. We introduce those effects with a superposition of Fokker-Planck solutions, i.e., by using an incident beam that contains a spectrum of initial energies, or equivalently, a set of csda ranges. Straggling effects appear to be a beam property in this approach but are returned to the material when we use it. All the information needed to construct the spectrum is obtained from a measurement of the electron rest charge distribution in polystyrene. To illustrate the correctness of this procedure, we consider the case of a 20 MeV electron beam incident on water. We predict the absorbed dose distribution as a function of depth and also measure it with an ionization chamber in a water tank. We find nearly perfect agreement between calculation and experiment in this case where all the results derive and apply to a clinically operational machine.