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In this study, the energy loss, range, and stopping time were calculated using the Bethe theory for protons in germanium and copper materials over an energy range of 0.01–1,000 MeV. The mathematical equations were programmed and implemented using MATLAB2013 to obtain the results for the relative mass stopping power and range, illustrated in tables and graphs. The computed results from the Bethe and Ziegler equations were compared with the experimental results from Pstar. The results showed a difference between the experimental and theoretical results at the beginning of the range used in the Bethe equation because it is a quantized equation that is not suitable for low energies. Hence, a correction term was proposed for the Bethe equation to correct the results at low energies, which produced negative values. On the other hand, the Ziegler equation showed good agreement along the range used as it is a semi-empirical equation. The range and stopping time of the incident particle increased with increasing incident particle energy in the mentioned materials.

Study of energy loss, range, and stopping time for proton in germanium and copper materials