Metallic Clusters

Large metallic clusters of heavy atoms are described within the quasi-classical theory, by means of a variational approach to the linearized Thomas-Fermi model. Effective inter-atomic potentials are derived and equilibrium spatial structures are given; these structures are universal for homo-atomic metallic clusters, in the sense that they are independent of the chemical nature of the atoms. The binding energies, inter-atomic distances, and the vibration spectra are computed as functions of the effective number of ”valence ” electrons; this effective valence is estimated from the atomic screening. Magic numbers are obtained, corresponding to close spatial packings; these geometric magic numbers are also universal for homo-atomic metallic clusters, in the sense that they do not depend on the atomic species. The quadrupole-deformed electronic potential of a cluster is also derived. The extension of the theory to including ionic or covalent bonds is discussed.