Influence of surface softness on supershell structure of metal clusters: Application to gallium

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Abstract
In order to interpret recent experimental results on gallium clusters, we investigate the influence of the surface softness on the electronic shell structure of spherical metal clusters. We discuss the physical reasons which support the introduction of a diffuse edge in the jellium model. We then perform quantum calculations using electronic potentials slightly modified as compared to the electronic potential obtained from self-consistent homogeneous jellium calculations. We show that the main influence of the diffuseness consists in the shift of the beating region in the supershell structure. A semiclassical analysis of this effect is also performed and the shift of the beating region is interpreted in a very simple way: the softness of the surface introduces a phase shift between the contributions of the classical triangular and square orbits to the density of states. This phase shift is roughly independent of the cluster size for a given diffuseness and this allows us to predict the shift of the beating region. Finally we discuss how we have to modify the uniform positive charge density of the standard jellium model to obtain results in agreement with the experiment and we show that the modification to be used for gallium is quite reasonable.