Calculation of electron trajectory and energy deposition in no screening region

The probability density function (PDF) of energy for inelastic collision is obtained by solving the integro-differential form of the quantity equation with the Bhabha differential cross section for particles with spin 1/2. Hence, the total PDF in no screening region is determined by folding theory with the following two assumptions: (1) the electron loses energy by collision and radiation and (2) the electron velocity does not change with a thin absorber. Therefore, a set of coupled stochastic differential equations based on the deviation and energy loss PDFs for electron is presented to obtain the electron trajectory inside the target. The energy PDFs for an electron beam with incident energy of 15.7 MeV inside aluminum and copper are calculated. Besides, the dose distributions for an electron beam with incident energies of 20, 10.2, 6, and 0.5 MeV in water are obtained. The results are in excellent agreement with the experimental data reported in the literature.