Periodic orbit theory for realistic cluster potentials: The leptodermous expansion

TL;DR

This paper develops a method to extend periodic-orbit theory to realistic cluster potentials by expanding around spherical wells, explaining supershell shifts in metal clusters with softer surfaces.

Contribution

It introduces a leptodermous expansion approach for realistic potentials, improving the understanding of supershell structures beyond simple models.

Findings

The leptodermous expansion accurately predicts supershell shifts.

Surface softness affects supershell structure.

Lattice contraction does not influence electronic shell structure.

Abstract

The formation of supershells observed in large metal clusters can be qualitatively understood from a periodic-orbit-expansion for a spherical cavity. To describe the changes in the supershell structure for different materials, one has, however, to go beyond that simple model. We show how periodic-orbit-expansions for realistic cluster potentials can be derived by expanding only the classical radial action around the limiting case of a spherical potential well. We give analytical results for the leptodermous expansion of Woods-Saxon potentials and show that it describes the shift of the supershells as the surface of a cluster potential gets softer. As a byproduct of our work, we find that the electronic shell and supershell structure is not affected by a lattice contraction, which might be present in small clusters.