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.

电子制止功率的一种广泛使用的表达方式是Bethe制止功率，它被用于许多应用中，例如辐射剂量测定法。各种研究都提出了近似Bethe停止力的解析解的方法。在这项研究中，之前从Gonzalez-Gaxiola研究中获得的解析解通过在实施拉普拉斯-阿都曼分解方法（LADM）之前使用相对论关系而扩展到了相对论能量。从LADM方法获得的级数解是所经过的路径长度和带电粒子的初始能量的函数。对于不同的入射能量，吸收介质和颗粒类型，我们的解决方案与数值模拟具有相对较好的一致性。