A Theoretical and Experimental Comparative Study of Proton Energy Loss in Various Elements and the Effects of Density Polarization and Shell Binding

Abstract

This research presents a comprehensive physical and computational model of the specific energy loss mechanism of incident protons over an energy range of 10 MeV to 1000 MeV in three elements with different compositions and atomic numbers: silicon (Si), copper (Cu), and gold (Au). This model employs a modified Beth-Bloch equation that considers the effects of density and shell structure. The dynamic characteristics of the incident proton's kinetics and its susceptibility to polarization and atomic bonding (shell structure) were investigated. The computational results and comparative analyses of the extracted computational tables demonstrate the crucial role of shell correction in suppressing low energies to prevent spikes in the theoretical calculations. This is achieved by considering the density Sternheimer correction limit as an electrostatic shielding barrier that ensures the stability of the radiation curve at high energies. The study adopted the precise log_10⁡βγ quantity to enhance the systems used in radiological medical planning and the development of nuclear shielding technologies, with results that closely match experimental reality.