Orientation-dependent retarding force of a three-dimensional degenerate electron gas for slow homonuclear trimers

A theoretical study is presented on the orientation-dependent retarding force experienced by a slow homonuclear linear trimer moving at arbitrary alignment with the direction of its flight in a three-dimensional degenerate electron gas of metallic densities. We apply a standard multiple-scattering method for elastic scattering of independent electrons off a three-center system in a screening environment. These centers are modeled by short-range auxiliary potentials and thus they are characterized by an effective $s$-type phase shift $\eta$. Within this framework for the orientation-dependent retarding force, the interplay of wave interference and multiple scattering is analyzed in a comparative manner for a realistic set of the input parameters. By allowing a restricted variation in the polar angle between the linear multicenter orientation and its velocity direction, a reasonable agreement with data obtained by a slow carbon trimer is established.

Figure 1

Illustrative dimensionless ratios $R_N^i$ showing the orientation dependence of renormalized stopping powers of a degenerate electron gas for a slow homonuclear linear trimer ($N=3$) and dimer ($N=2$) under parallel ($\parallel$) (solid curves) and perpendicular ($\perp$) (dashed curves) conditions of traversing the target material. The curves are exhibited for the $x\in [0,7]$ mathematical range, where $x=k_{F}d$. They are calculated from Eqs. (8) and (9), i.e., by neglecting the effect of multiple scattering, but considering wave interference.

Figure 2

Dimensionless ratios $R_N^i$ showing the orientation dependence of renormalized stopping powers of a degenerate electron gas for a slow linear carbon trimer ($N=3$) and dimer ($N=2$). The conventions of Fig. 1 are used. The dotted curve in the upper panel is based on Eq. (11). The curves are computed by considering wave interference and multiple scattering simultaneously. The shadowed area around the dotted curve brackets the $\alpha \in [\pi /8,\pi /4]$ angle interval. The effective [6, 19] phase shift employed is $\eta =2.3$. The experimental data (with error bars) are exhibited by filled squares. See the text for further details.