Rough droplet model for spherical metal clusters

TL;DR

This paper models surface roughness in metal clusters using a liquid drop approach, deriving an expression for roughness as a function of temperature and size, and compares results with experimental shell energy data.

Contribution

It introduces a simple analytic model for surface roughness in metal clusters and links it to shell structure effects, providing a new perspective beyond Jahn-Teller deformations.

Findings

Surface roughness parameter $$ approximates experimental shell energy attenuation.

Roughness model reproduces experimental shell energy shapes for sodium clusters.

Surface roughness decreases shell structure amplitude consistent with observations.

Abstract

We study the thermally activated oscillations, or capillary waves, of a neutral metal cluster within the liquid drop model. These deformations correspond to a surface roughness which we characterize by a single parameter $\Delta$. We derive a simple analytic approximate expression determining $\Delta$ as a function of temperature and cluster size. We then estimate the induced effects on shell structure by means of a periodic orbit analysis and compare with recent data for shell energy of sodium clusters in the size range $50 < N < 250$. A small surface roughness $\Delta\simeq 0.6$ \AA~ is seen to give a reasonable account of the decrease of amplitude of the shell structure observed in experiment. Moreover -- contrary to usual Jahn-Teller type of deformations -- roughness correctly reproduces the shape of the shell energy in the domain of sizes considered in experiment.