Supershells in Metal Clusters

In the mass spectra of elemental clusters one observes oscillations in the abundance as a function of cluster size. These oscillations reflect variations $\tilde{E}$ in the total energy of the clusters. In most cases $\tilde{E}$ is determined by the geometric arrangement of the atoms. For simple metals at temperatures above the melting point, however, the electonic structure is dominant, giving rise to electonic shells and supershells. Using a jellium model for systems of up to 10000 electrons, the experimental findings for alkali clusters can be reproduced fairly well. But in the case of gallium that simple model fails. To gain insight into the mechanisms determining the shell and supershell structure, we extend the known semiclassical analysis for the DOS of a spherical cavity to more realistic potentials. This suggests a simple mechanism for explaining the failure of the jellium model for metals with high electron density.

For a quick overview, take a look at these Slides taken form a talk on the subject (1MB)

More detailed information can be found in the following publications

Supershells in Metal Clusters: Self-consistent Calculations and their Semiclassical interpretation, Phys. Rev. Lett. 76, 2678 (1996)
On the 3n+l Quantum Number in the Cluster Problem, Phys. Rev. A 54, 670 (1996)
Density Dependence of the Electronic Supershells in the Homogeneous Jellium Model, Phys. Rev. B 54, 5168 (1996)
Periodic Orbit Expansion for Realistic Cluster Potentials: The Leptodermous Expansion, in preparation

Die folgenden Postscript-Dateien enthalten die einzelnen Kapitel meiner Dissertation mit dem Titel:

Superschalen in Metallclustern:

Selbstkonsistente Rechnungen und ihre semiklassische Interpretation

Abstract und Inhaltsverzeichnis (69 KB)

Einführung (86 KB)

Kapitel 1: Pseudo-Quantenzahl (126 KB)

Kapitel 2: Jellium-Modell (218 KB)

Kapitel 3: Jellium-Ergebnisse (450 KB)

Kapitel 4: Semiklassik (289 KB)

Kapitel 5: Cluster-Kontraktion (117 KB)

Kapitel 6: Leptoderme Entwicklung (153 KB)

Schlußbetrachtung (68 KB)

Anhang A: Linearisierung der Integrale (103 KB)

Anhang B: Maslov-Phase (74 KB)

Literaturverzeichnis (70 KB)

all in one (1.2 MB)

Die vorliegende Arbeit wurde am Max-Planck-Insititut für Festkörperforschung, Stuttgart in der Arbeitsgruppe von Prof. O.K. Andersen unter der Anleitung von Dr. O. Gunnarsson angefertigt.

Meine Diplomarbeit mit dem Titel Bosonische Darstellungen Minimaler Modelle beschäftigt sich mit Konformen Feldtheorien in zwei Dimensionen.

Erik Koch (koch@and.mpi-stuttgart.mpg.de)