Using Relativistic Kinematics to Generalize the Series Solution of Bethe Stopping Power Obtained from 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 of Gonzalez-Gaxiola was extended to relativistic energies by using relativistic relations prior to implementation of Laplace-Adomian decomposition method (LADM). The series solution obtained from LADM method is a function of path length traversed and 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.