Electron dose calculation using multiple‐scattering theory: A new theory of multiple scattering

Starting from the Boltzmann–Fokker–Planck transport equation, we have developed a new theory of multiple scattering which incorporates the advances already made with our Gaussian multiple‐scattering theory for electron dose calculation. This incorporation has been accomplished in a natural way, by modifying the scattering power T and by adding a convolution term to the distribution‐function equation of the Gaussian theory. Our previous results concerning increasing the accuracy of the small‐angle approximation used and dealing with localized tissue inhomogeneities have thus been maintained, and we have arrived at a complete distribution function in both transverse spatial and angular variables. When integrated over the transverse angular variables, for a first‐order small‐angle approximation this distribution function for a pencil beam is essentially the same as the Molière multiple‐scattering distribution, which includes large‐angle single scattering. For a water phantom, we have used comparisons with EGS4 Monte Carlo calculations to demonstrate the greatly increased accuracy of our new multiple‐scattering theory over the Gaussian theory, which includes the usual Fermi–Eyges theory. We have also presented a fairly accurate Gaussian approximation to the pencil‐beam dose profiles given by our new theory, which can be used in order to maintain the mathematical simplicity of the predictions of the Fermi–Eyges theory.