We discuss thephysical properties of a non interacting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential,and its electric static polarizability. All these properties are discussed analytically as functions of the number N of electrons. The trends obtained with increasing N are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasi spherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the de\ufb01nition of a scale-invariant distribution of magic numbers which follows a power law with critical exponent 120.5. We conclude that our completely mechanistic and analytically tractable model can be useful for the analysis of self-assembling complex systems
