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We discuss the physical properties of a noninteracting 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 quasispherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the definition of a scale-invariant distribution of magic numbers which follows a power law with critical exponent $\ensuremath{-}0.5$. We conclude that our completely mechanistic and analytically tractable model can be useful for the analysis of self-assembling complex systems.

The dynamics of an electron wave packet in the presence of laser radiation and of a one-dimensional repulsive soft-core potential is investigated. For different laser intensities and for different initial positions of the electron wave packet, these results are compared with those for an attractive potential. The repulsive potential is capable of confining the electron quite efficiently under appropriate conditions. In these conditions, the electron is shown to emit a high harmonic spectrum similar to that emitted by the more conventional attractive potential. It is thus argued that recombination into an atomic bound state as required by the three step model is not essential for the emission of high harmonics.