Energy loss of protons in Au, Pb, and Bi using relativistic wave functions

Abstract

We present a theoretical study on proton energy loss in solid targets of atomic number greater than 54. Fully relativistic wave functions and binding energies are obtained by solving numerically the Dirac equation. Ab initio calculations are developed for the first stopping and second straggling moments of the energy transferred from the ion to the target electrons. The shellwise local plasma approximation is employed for the inner shells, and the Mermin dielectric function is employed for the valence electrons. The dielectric response of each subshell is calculated separately, including in this way the screening among the electrons of the same binding energy. Results for stopping and straggling cross sections of protons in Au, Pb, and Bi are compared with the available experimental data. The theoretical stopping results are very good in the case of Au, reproducing the experimental data in an extensive energy region 10 keV‐100 MeV. For Pb and Bi, the stopping results agree with the measurements for energies above 300 keV, for which the inner shells play a major role. However, we found some difficulties around the stopping maximum. For the energy-loss straggling, we obtained reasonably good agreement with the experiments for the three targets studied.