Cresting the Coulomb Barrier of Polyanionic Metal Clusters

Combining photoelectron spectroscopy with tunable laser pulse excitation allows us to characterize the Coulomb barrier potential of multiply negatively charged silver clusters. The spectra of mass- and charge-selected polyanionic systems, with $z=2–5$ excess electrons, show a characteristic dependence on the excitation energy, which emphasizes the role of electron tunneling through the barrier. By evaluating experimental data from an 800-atom system, the electron yield is parametrized with respect to tunneling near the photoemission threshold. This analysis results in the first experimentally based potential energy functions of polyanionic metal clusters.

Figure 1

Photoelectron spectra of ${\mathrm{Ag}}_{800}^{3-}$ for different laser photon energies $E_{\mathrm{ph}}$. The shown yields are $Y/S$, i.e. normalized by $S$ to account for absorption-dependent effects, for details see text. The common signal onset and the strong increase in the yields with $E_{\mathrm{ph}}$ indicates tunneling through the Coulomb barrier. Inset: The excess electrons in the PAC lead to the formation of a Coulomb barrier at the cluster surface. Direct photoemission from the electronic level system (shaded grey), as well as tunneling, may contribute to the spectra.

Figure 2

PES of ${\mathrm{Ag}}_{800}^{z-}$, $z=2–5$ (colored lines), with laser excitation energies as indicated. All curves are displayed on a logarithmic scale and normalized with respect to $S$. Plotting Eq. (2) with the mean values of $ϵ$ and $T$ from the fits to the measured PES (Table 1) results in the black curves. Figure 2 shows the respective data of Fig. 1, with the vertical dashed line denoting exemplarily the extracted Coulomb barrier height $V_{\max }$ with its uncertainty range marked in grey. Multi-photon absorption-induced photoemission cannot completely be suppressed, as seen by the dotted contributions.

Figure 3

Potentials $V(r)$ obtained from fitting the experimental spectra of ${\mathrm{Ag}}_{800}^{z-}$ with Eq. (2). These single-particle potentials correspond to the ($z-1$)-fold charged systems remaining after photoemission. The respective barrier heights $V_{\max }$ are compiled in the inset.