Highly accurate ab initio electronic stopping power results for protons in Al material: a Lindhard stopping theory investigation

Abstract The main goal of this work is to enhance theoretical precision evaluations for the random electronic stopping power (RESP) of protons in solid targets across a wide range of energies, including low, intermediate, and high energies. The RESP of protons is investigated in different crystalline forms of Al material: FCC and two theoretical build structures (hexagonal and tetragonal). Initially, we divide the RESP calculations of protons in Al material into two individual contributions: one for the valence electrons and the other for the core electrons. Using this approach, we introduce a combination method that defines the total RESP as the sum of these contributions. We estimate the core electrons’ contribution to the RESP results within the local density approximation (LDA) based on the Lindhard stopping theory, where we calculate the density of Al material within the density functional theory (DFT) framework. We employ the RESP contribution of valence electrons as determined in our previous study within the linear response time-dependent density functional theory. We produce high-quality RESP results with the assistance of the combination method with low computational cost compared to other theoretical works. We test the accuracy of using the LDA based on Lindhard’s stopping model in calculating the RESP of protons in the Al target. In addition, within this approach, we investigate the influence of the crystal structure on core electrons’ contribution to the RESP.