Shape effect and quantum size effect on small metal particles

The electronic properties of small metallic particles are expressed by the generalized formula that incorporates the effect of particle shape in addition to the quantum size effect in such a way as to connect the Poisson distribution and orthogonal distribution from random matrix theory. The experiments on the static magnetic susceptibility of small magnesium particles recently obtained were analyzed by means of the proposed formula and were well explained assuming the regularity of particle shape. The observation by high resolution electron microscopy suggests that many particles are not rough in shape. This is inconsistent with commonly accepted assumptions made about small metallic particles. 'The degree of metallicity' is introduced to characterize the statistics of level spacing fluctuation of small metal particles and this divides the statistics into four typical regions: Bulk metal with Fermi-Dirac statistics, small metallic particles with Poisson statistics, small particles with Wigner-Dyson statistics and insulating molecules. The relation of lattice disorder to the shape effect is briefly discussed taking into account the effect of Anderson localization. (orig.)