Size-Dependent Electron-Impact Detachment of Internally Cold $\mathrm{C}_n{}^{-}$ and $\mathrm{A}\mathrm{l}_n{}^{-}$ Clusters

The cross sections for electron detachment of internally cold $\mathrm{C}_n{}^{-}$ and $\mathrm{A}\mathrm{l}_n{}^{-}$ clusters were measured using an electrostatic ion beam trap fitted with an internal electron target. The measured electron-impact detachment cross sections for the $\mathrm{C}_n{}^{-}$ ($n=1–9$) clusters exhibit even-odd oscillations reflecting the binding energy trend, namely, higher cross sections for weaker binding. Surprisingly, however, these cross sections increase on the average with cluster size, $n$, in spite of the increase in electron binding. In contrast, the $\mathrm{A}\mathrm{l}_n{}^{-}$ ($n=2–5$) clusters follow the known scaling laws for electron detachment. We suggest that the size-dependent polarizability of these clusters is responsible for the observed behavior.

Figure 1

Schematic view of the experimental setup. The diameter of the chamber is 451 mm.

Figure 2

Measured cross sections ${\sigma }_e$ at $E_e=20\mathrm{e}\mathrm{V}$ as a function of the number of atoms $n$ for (a) $\mathrm{C}_n{}^{-}$ (solid squares connected by a line) and (b) $\mathrm{A}\mathrm{l}_n{}^{-}$ (solid triangles connected by a line). Also shown are the calculated cross sections for $\mathrm{C}_n{}^{-}$ (open squares connected by a dashed line) and $\mathrm{A}\mathrm{l}_n{}^{-}$ (open triangles connected by a dashed line) using the theory of Andersen et al. [13, 15]. Data and theory are normalized to the absolute cross section of $\mathrm{C}_n{}^{-}$ [28]. The filled circles (a) are the measured absolute cross sections for $\mathrm{C}$ [29] (interpolated to 20 eV) and $\mathrm{C}_4{}^{-}$ [30]. Insets: electron binding energy for (a) carbon and (b) aluminum clusters as a function of $n$ [20, 22]. (c) Ratio between the experimental and theoretical cross sections for $\mathrm{C}_n{}^{-}$ (squares) and $\mathrm{A}\mathrm{l}_n{}^{-}$ (open triangles) at $E_e=20\mathrm{e}\mathrm{V}$ as a function of $n$. The theoretical cross sections ${\sigma }_e^{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}}$ were computed using the functional dependence on the electron binding energy, as suggested by Andersen et al. [13, 15]. The lines are drawn to guide the eye.