Using relativistic kinematics to generalize the series solution of Bethe stopping power obtained from Laplace-Adomian Decomposition method
A. S. Remigio
Royal Melbourne Institute of Technology University, Melbourne, 3000 Victoria, Australia
Abstract
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.