Ground- and excited-state scattering potentials for the stopping of protons in an electron gas

Abstract

The self-consistent electron-ion potential V(r) is calculated for H + ions in an electron gas system as a function of the projectile energy to model the electronic stopping power for conduction-band electrons. The results show different self-consistent potentials at low projectile-energies, related to different degrees of excitation of the electron cloud surrounding the intruder ion. This behavior can explain the abrupt change of velocity dependent screening-length of the potential found by the use of the extended Friedel sum rule and the possible breakdown of the standard free electron gas model for the electronic stopping at low projectile energies. A dynamical interpolation of V(r) is proposed and used to calculate the stopping power for H + interacting with the valence electrons of Al. The results are in good agreement with the TDDFT benchmark calculations as well as with experimental data.

Stopping power of cluster ions in a free-electron gas from partial-wave analysis

“…Linear predictions calculated using Eqs. (19) and (20) are in strong disagreement with experimental data by almost a factor of 2 at low energies for He as a companion ion. Thus, linear interaction models should overestimate the stopping-power ratio in Fig.…”

“…A nonperturbative model for the vicinage effect on the stopping power of cluster ions in matter (IDAMol) was developed by generalizing the stopping-power formula (IDA model) derived recently [18,19] for ions slowing down in an electron-gas system. For this sake it was assumed that the cluster orientation is not aligned to any particular direction and a general expression Eq.…”

“…which is notably different from the transport cross-section (TCS) approach, which is based on the momentum transfer cross section [20][21][22]. Both formulas are nonperturbative and able to describe nonlinear effects on the stopping power of ions in FEG system very well [19]. However, the TCS approach has a very slow convergence of the results to the expected Bethe formula, while the IDA approach tends to overestimate the stopping values at low energies.…”

“…As demonstrated recently by IDA calculations [19], the best choice for the electron-ion potential is the Yukawa potential with inverse of screening length α obtained from a dynamical interpolation between the high-velocity solution α = ω p /v and the values for the static limit α 0 as obtained by DFT with exchange-correlation terms. Such results have a rather good agreement with full TDDFT calculations for a wide range of projectile energies.…”

“…Recently, an approach has been developed to evaluate the electronic stopping power and the transport cross section in electron-ion collisions, namely the induced density approach (IDA) and applied to H + ions in a free-electron gas (FEG) [18,19]. The stopping power is calculated by the retarding force caused by the asymmetric induced charge density on the projectile.…”