On the scattering power of radiotherapy protons

Scattering power (T = d/dx of mean squared multiple Coulomb scattering (MCS) angle), as used in proton transport theory, is properly viewed as a differential description of the Gaussian approximation to MCS theories such as Moliere's. That is, we seek a function T which, when integrated over a finite slab, will recover the Moliere/Fano/Hanson angle for that slab. To be accurate, T must include a single scattering correction, which means mathematically it must be nonlocal, depending on how much MCS has taken place as well as the energy and scattering material at the POI. We review five formulas for T and introduce a sixth, testing each against the Moliere/Fano/Hanson prediction as well as experimental data. We discuss how sensitive some practical problems are to the choice of T. That choice is probably most important for general Monte Carlo codes, which are expected to address a wide variety of problems.