The screening and stopping coefficients of slow light ions

Abstract

We present a theoretical approach to study the screening charge density n(s)(r) and the respective stopping coefficient Q for hydrogen and helium at the low velocity limit. An electron gas, with electronic density n(e), is used to represent the conduction or valence electrons of the target material. Solving numerically the Schrödinger radial equation, for a given potential V (r), the phase shifts δ(l) and the corresponding stopping coefficient Q are calculated as a function of n(e). The cusp condition and the Friedel sum rule are imposed on the charge density n(r) = n(s)(r)+n(e) at the origin and to the phase shifts, respectively. The results are compared with density functional calculations and with available experimental results.

Electronic Excitations of Slow Ions in a Free Electron Gas Metal: Evidence for Charge Exchange Effects

“…Our results are in very good agreement with earlier measurements [27] (open squares) and at the same time extend the range, where " / v is observed, by a factor of 2 towards lower energies. For H projectiles, our data are in perfect agreement with theoretical calculations for a FEG [34,35] with a density parameter r s of 2.13, appropriate for Al [36] (gray dotted line). From this, it can be concluded that excitation of electron-hole pairs in binary collisions along the ion trajectory is the only relevant energy dissipation mechanism active when slow H ions move in Al.…”

“…For instance, for a dilute FEG, DFT predicts that He ions should be less efficiently decelerated than H ions, in contrast to experimental findings [34,35,42]. For Mg, H and He ions were predicted to experience the same deceleration force, while much stronger stopping was observed for He ions.…”

“…Also shown are data from [27,37]. Predictions from DFT for slow H and He in a FEG are shown as dotted and dashed gray lines, respectively [34,35].…”

Electronic interactions of medium-energy ions in hafnium dioxide

“…In terms of an effective electron density this would correspond to more than 11e − contributing to the electronic stopping in the case of He, if the energy-loss processes were due to the creation of electron-hole pairs exclusively, i.e., three times more electrons participating in the energy-loss processes. Note that, depending on details in the modeling, DFT approaches can also yield slightly different values for the density parameter [59]. In fact, the modeling from the latter group results in a value of r s = 1.62 for He whereas hydrogen data agree well with r s = 2.3 (see the dashed line in Fig.…”

Topological invariants in interacting quantum spin Hall: a cluster perturbation theory approach

“…They have found an unified language within the variational scheme based on the the Self Energy Functional approach [27]. These methods, with different degrees of accuracy, give access to non trivial many body effects and have been applied both to model systems and to realistic solids [28,29].…”