Periodic orbit theory for realistic cluster potentials

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. 71.24.+q, 31.15.Gy

Quasiclassical description of electronic supershells in simple metal clusters

“…One can suppose from here that a periodic-orbit-expansion (or supershellexpansion), obtained for a spherical cavity, is a particular case of the more general expansion for spherical cluster potentials. This conclusion is supported in the recent paper [8] where such a generalization was carried out using Woods-Saxon potential by expanding on a parameter a/R (a is a surface width) around the known results for a spherical potential well. It is of interest to investigate analytically the origin of supershells and the mechanisms leading to their appearance for a potential of arbitrary form.…”

“…In Eqs. (8) and (9) the symbol j numerates a kind of the electronic orbit: j = 0 corresponds to the linear pendulating orbit, the terms j ≥ 1 (K ≥ 3) are connected with the planar regular polygons, K being the number of their vertices. The integer value s is equal to a number of periods that the electronic trajectory (j, s)…”

“…includes, so the sum over s is the trajectory length-expansion for a j-orbit (compare with the orbits (λ, ν) in Ref. [8]). 4.…”