On the universal scaling in the electronic stopping cross section for heavy ion projectiles

Abstract

Energy deposition of heavy ions when penetrating a material is of crucial importance in determining the damage to materials with implications in areas such as material science, plasma physics, radiotherapy and dosimetry. Due to the N-body electron problem, it has been thought that the electronic stopping cross section is unique for a given projectile-target combination and differs from system to system. In this work, we show that within the Bethe theory, there is a universal scaling when the electronic stopping cross sections and projectile kinetic energy are scaled properly in terms of the target mean excitation energy, I 0 , for all projectile-target combinations. We show that the scaling is given by I 0 S e /π e 4 Z * p as a function of m e E p /M p I 0 , thus showing the importance of the characterization of the mean excitation energy. The scaling law expresses a systematic and universal behavior among complex projectile-target systems in the energy deposition, characterized by the minimum momentum transfer during the slowing down process. We provide an analytic expression for the universal scaling law for the stopping cross section of any projectile-target combination valid at high collision energies. Finally, we verify the universal scaling law by comparison to atomic and molecular experimental data available in the literature. We expect our findings will motivate further experimental work to verify our universal scaling for more complex systems in the absence of experimental data. ARTICLE HISTORY