Rough droplet model for spherical metal clusters

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 ∆. We derive a simple analytic expression determining ∆ 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 ∆ ≃ 0.7 Å is seen to give a good account of the decrease of shell structure observed in experiment. PACS numbers : 36.40.+d Atomic and molecular clusters. 71.20.–b Electron density of states. 03.65.Sq Semiclassical theories and applications. IPNO/TH 97-19 submitted to Phys. Rev. B 1 Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS.