Using Relativistic Kinematics to Generalize the Series Solution of Bethe Stopping Power Obtained from the Laplace–Adomian Decomposition Method

One widely used expression of electronic stopping power is the Bethe stopping power, which is used in many applications such as radiation dosimetry. Various studies have presented methods to approximate the analytical solution of the Bethe stopping power. In this study, analytical solution obtained previously from the study by Gonzalez-Gaxiola et al. is extended to relativistic energies by using relativistic relations prior to implementation of the Laplace–Adomian decomposition method (LADM). The series solution obtained from the LADM method is a function of the path length traversed and the initial energy of the charged particle. Our solution results in relatively good agreement with numerical simulation for different incident energies, absorbing media, and particle types. Plots of relative difference illustrate increasing deviations between LADM and numerical solution towards the end of the particle range due to exclusion of higher order terms.