Big Experiment for Research on Temperature controlled cluster Anions and cations (Berta)

Researching PhD student: Lukas Weise

The total setup

Sodium and aluminum clusters were produced in an evaporation respectively magnetron sputter source. For sodium atoms were evaporated from an oven, condensed to clusters in a liquid-nitrogen cooled He gas flow, and ionized by an electric discharge.

The clusters were trapped in a 12-pole RF ion trap connected to a cold-head for two purposes: The trap accumulates ions from the continuously running source and bunches them to much higher intensities, and the trap serves to cool clusters via thermalization with buffer gas atoms (~10-3 mbar He, trap temperature 6K). Single mass clusters were selected with a multi-wire mass gate at the first time-focusing point of a time-of-flight spectrometer. By crossing the cluster beam with a laser beam, photoelectrons were detached from the cluster ions and guided to a two-dimensional electron detector (single MCP and phosphor screen) while expanding according to their initial velocities. The resulting electron distribution were recorded with a fast CCD camera from the outside of the vacuum chamber.

Experimental results for Sodium clusters


  • For all investigated cluster sizes the β parameters show a smooth evolution with the excitation energy.
  • Especially for bigger sizes β reaches strongly negative values. This can only occur by the interference of two outgoing partial waves which leads to the assumption of a high coherence during the excitation process, even for very big many-particle systems as Na147-.

Comparison of the approximate angular momentum eigenstates for different cluster sizes

  • Characteristic differences exist for the evolution of β parameters of jellium states with different l quantum numbers.
  • Energetically split jellium states from the same cluster size show a very similar evolution of β if plotted versus the kinetic energy of the detached electron.
  • Another similarity is observed between β parameters for jellium states with the same l quantum number but from different cluster sizes.
→ The interaction of the electrons with the ionic background evidently only modifies the energies of the different states, but not the overall character of the wave functions.
→ The quantum number l still satisfyingly characterizes the bound states even for nonspherical symmetries.

Theoretical background

A lot of information about the electronic and geometric structure of clusters has been extracted from photoelectron spectroscopy (Wrigge et al, PRA 65, 063201, 2002; Häkkinen et al, PRL 93, 093401, 2004).The experimental results for alkali metal clusters are in excellent agreement with the jellium model for the electronic states.

In the single active electron picture (i.e. the photon effectively interacts with a single electron) the angular distributions of photodetached electrons should be influenced by the angular momentum quantum number of the bound state and therefore can provide further information about the accuracy of this model.

Assuming effective single particle potentials for the bound states, the angular distribution of photoelectrons for one-photon excitation with linearly polarized light can be described by a single anisotropy parameter β. This parameter can be calculated using the Cooper-Zare formula.
Calculations were done for box type and Woods-Saxon type effective potentials (analytically and numerically). The β parameter shows a strong dependence on the excitation energy and the initial state angular momentum. Although there is no direct agreement with the performed calculations, the measured curves show the same behavior

Data of Ag55 and Cu55 clusters and comparing with Na55

  • Splitting of 1g and 1f level because of icosahedral structure.
  • In contrast to sodium and copper the both outer peaks of silver don't overlay.
  • DFT calculations show very similar electron densities for silver and sodium.
  • Peaks of the 1g level: compared to sodium the minima of the distributions of copper and silver are shifted to higher kinetic energies.
  • Peak of the 2p level: the distributions of copper and silver are very similar.
  • Minima of the Betaparameter distributions are similar when plotted against the kinetic energy multiplied by the clustersize.