Slow heavy dimers in a two-dimensional degenerate electron gas: Calculation of orientation-dependent retarding forces

We present a theoretical study on the orientation-dependent retarding force experienced by slow dimers moving at arbitrary alignment with the direction of their velocity in a two dimensional degenerate electron gas. The influence of the individual constituents of a dimer on independent electrons is modeled by effective, $s$-type phase shifts $\eta$. Analytical results are derived by considering the effects of interference and multiple scattering. The orientation-dependent expressions reveal the dependence of stopping power on the classical geometry and these effects of quantum dynamics. A brief account on strongly related problems of resistivity caused by imperfections in the many-body system and pure dephasing of elastically scattered electrons is made, as well. The physically motivated case of $\eta \left(k_F\right)=\pm \left(\pi /2\right)$ for the leading phase shift is explicitly discussed.

Figure 1

Illustrative ratios, denoted as $g_r^i\left(D,x\right)$, showing the orientation dependence of renormalized stopping powers of $D$ dimensional degenerate electron gases for in-moving slow homonuclear dimers. The parallel $(\parallel )$ (solid curves), perpendicular $(\perp )$ (dashed curves), and random (dotted curves) cases refer to fixed angles (see the text) between dimer orientation and its velocity direction. The curves are exhibited for the $x∊\left[0,7\right]$ range, where $x=k_{F}d$. The upper panel is devoted to the two dimensional $\left(D=2\right)$ case, while the lower panel (based on Ref. 14) to the three dimensional $\left(D=3\right)$ one. All curves are obtained in the perturbative impulse approximation.

Figure 2

Illustrative ratios, denoted as $G_r^i\left(D,x\right)$, showing the orientation dependence of renormalized stopping powers of $D$-dimensional degenerate electron gases for in-moving slow homonuclear dimers. The parallel $(\parallel )$ (solid curves), perpendicular $(\perp )$ (dashed curves), and random (dotted curves) cases refer to fixed angles (see the text) between dimer orientation and its velocity direction. The curves are exhibited for the $x∊\left[0,7\right]$ range, where $x=k_{F}d$. The upper panel is devoted to the two dimensional $\left(D=2\right)$ case while the lower panel (taken from Ref. 14) to the three-dimensional $\left(D=3\right)$ one. The curves are obtained beyond the perturbative (cf., Fig. 1) impulse approximation, by considering the modulating effect of multiple scattering with $\eta =\pi /2$.