Stopping power of a degenerate electron gas for slow ions: Influence of relative kinematics on $Z_1$-oscillation

Based on the kinetic theory of stopping of a homogeneous electron gas for heavy ions with nuclear charge $Z_1$, the intrinsic role of relative-kinematics in averaged binary energy transfers is investigated. The required quantum mechanical transport cross sections are computed with self-consistent screened potentials obtained in the Kohn-Sham mean-field approximation at embedding condition. Important changes, as a function of intruder velocities, are established in the $Z_1$-oscillation of the resulting theoretical stopping. The changes signal the need for a proper consideration of relative kinematics in predictions for inelastic energy losses in electron gases even at moderate ion-velocities, and suggest further studies to include atomistic channels to a complete understanding.

Figure 1

Theoretical, radial electron densities around $(Z_1=10)$ as obtained with the Kohn-Sham method at different environment conditions. The solid curve refers to the embedding scheme $(r_s=2)$, while the dashed one to a neutral atom.

Figure 2

Normalized effective potentials, $-r{V}^{\left(\mathit{sc}\right)}\left(r\right)∕Z_1$ and $-r{V}^{\left(m\right)}\left(r\right)∕Z_1$, for Ne and Zn. Solid curves refer to the embedding scheme $(r_s=2)$, while the dashed ones to neutral atoms.

Figure 3

Stopping characteristics, in the form of $[dE∕dx]∕v$, at different common velocities $\left(v\right)$ of intruders $Z_1∊[1,40]$. The density of the electron gas is prescribed by $r_s=2$. The embedding Kohn-Sham method with exchange-correlation is used. Open, half-filled, and solid circles refer to the $v\to 0$, $v=0.5$, and $v=1.0$ velocities, respectively.

Figure 4

Comparison of different predictions for the stopping power of an electron gas $(r_s=2)$ at a fixed velocity $(v=0.7)$ of intruders $Z_1∊[1,40]$. Open circles are based on the $V^{\left(\mathit{sc}\right)}\left(r\right)$ while the open triangles with a cross on the $V^{\left(m\right)}\left(r\right)$ potentials. Stars refer to experimental points of Ref. 6.