A study of threshold effects in the energy loss of slow protons in semiconductors and insulators using dielectric and non-linear approaches

The energy loss of slow protons in nonconducting materials, including semiconductors and insulators, is studied using different theoretical methods. First we apply two dielectric models proposed by Brandt and Reinheimer on one side, and by Levine and Louie on the other, and describe in detail the properties of individual and collective contributions according to each model. In addition, we perform an alternative calculation using a non-linear approach based on transport-cross-section methods. These different approaches are compared with experimental results for two semiconductors (Si and Ge) and two insulators (LiF and AlF3), obtaining an approximate description of threshold effects at very low energies. Some interesting similarities and discrepancies are found, which show the current limitations of the theoretical descriptions provided by these methods.